HOW TO MAKE A BOOK OF BIDDING SEQUENCES

A Book of Bids, given its size, has to a be virtual book accessible maybe via a web application. The computational challenge is presented here. In principle it not hard just laborious. A previous attempt at publishing a real app was successful from a technical perspective but with page number references possibly 46 digits long it was unwieldy. Page selection would need be randomized to engage the curious.

A complete Book must have be a page for each possible complete sequence and there must be an ordered continuous mapping of sorts that ties the page to a sequence. There can be no gaps or blank pages. However a quarter size book can be obtained by setting aside the trivial 4 lead-in call sequences (see above) and catalogue just the bid sequences with the 7 exits. These are generic sequences. Still there must be a continuous mapping, no gaps or empty pages. A mapping template for 21 possible bid transitions is best developed with base22 arithmetic. This clarifies the detail of the mapping. note: the mappings below have the hand-passed-out sequence also set aside. note:decimal values are in parenthesis

Once Page and Sequence are logically ordered the same delta value applies to all sequences in the group tied to a specific last-bid position [m] - Consider the sequence encoding 7C DFK L5H₂₂

There are two calcuation methods: subtract the group delta containing the sequence or subtract the group start sequence and add the group start page. The latter, of course, is how the group delta is determined in the first instance.
7C DFK L5H₂₂ is on page 6JL166C3₂₂ which is page 24711966755₁₀ decimal.
The hand_passed_out sequence can be assigned page 0. If there is an aesthetic objection increment all page numbers by 1 and position hand_passed_out on page 1. Regardless the short book has no page numbering gaps and all legal sequences are included.

THE BIGGER BOOK
The remaining task is to construct a book with ABSOLUTE pages that reference all the complete sequences including inter-bid transitions, exit calls but in addition combines the 4 lead-ins. The pages must still retain the property that each is tied to a unique complete bidding sequence, all complete sequences are included and there is continuous mapping, no gaps, duplicates or blank pages.

The direct approach is a book organized with 4 chapters (a chapter for each lead-in) but each chapter's contents are effectively duplicated containing the same generic sequences . The chapters are constructional artifices and not necessarily declared. The generic sequence page number is added to page number displacement of the start of each psuedo chapter.
++++

T is 7x (22^35-1)/(22-1)==1/3 (22^35-1)
T=32186412586757670780057981527902342840780674389

DECOMPOSING AN ABSOLUTE-PAGE NUMBER

Mathematical Caution: Conventionally page numbers are ordinals, page 1 is the first page, page2 is the second and so. Arithmetic is mostly cardinal. 6 pages per chapter then page 9 is the 3^rd page of chapter 2, but 9/6 = 1 remainder 3, so the chapter number must be incremented.
The books of bids has pseudo chapters that should go from 0 to 3 to show the lead-in passes but if the absolute-page is divisible by T then the Lead will be 1 more. 1 is subtracted from the abs-page prior to appying the QuotientRemainderFunction to get the lead passes correct but then the local or generic sequence page number must be adjusted after.
The whole method is straightforward once the delta is determined and the PLO and PHI functions make that step clear.
QuotientRemainderFunction[a,b] → a/b expressed as an integer q with remainder r < b
QuotientRemainderFunction[abs_page-1,T] → {#lead-in passes (0 ↔ 3), cardinal-page(0 ↔T-1)}

abs-page = 99650 60937 376867 72014 909535 75984 73706 44847 88610₁₀.
QRF[abs_page-1,T]
# lead-in passes =3
cardinal-page=3091371613495664861317008992277708542142765443₁₀
ordinal-page=3091371613495664861317008992277708542142765444₁₀ 'add 1'
o-page22=Base22[c-page] 'convert to base22 as list'
{15,10,19,17,0,1,4,2,18,10, 19, 0, 9, 18, 8, 6, 7,3,2,8,0,1,5,14,3,14,9,4,3,15,19,1,12,0}₂₂

{F, A, J, H, 0, 1, 4, 2, I, A, J, 0, 9, I, 8, 6, 7, 3, 2, 8, 0, 1, 5, E, 3, E, 9, 4, 3, F, J, 1, C, 0}₂₂ [34 bids]
PLO[34]=__{7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8}₂₂
PHI[35]= {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7}₂₂
___________________{E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E,E}₂₂
E[34]= 2926037507887060980005271047991122076434606762
SEQ=NP+E[34] → 6017409121382725841322280040268830618577372206. In list form
{1, 8, 3, C, 9, E, F, I, H, B, 3, B,F C, B, 0, K, L, H, H, 0, E, G, 8, 6, I, 7, 1, J, 6, 8, B, G, 4, E}₂₂
[35 bids]
The remaining step is to expand the sequence in bid speak using the reference tables tables below.

Bid speak requires that the order of the encoding is reversed so the little bids appear first.