Best Known (91, s)-Sequences in Base 2
(91, 52)-Sequence over F2 — Constructive and digital
Digital (91, 52)-sequence over F2, using
- t-expansion [i] based on digital (90, 52)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 4 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(91, 56)-Sequence over F2 — Digital
Digital (91, 56)-sequence over F2, using
- t-expansion [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
(91, 99)-Sequence in Base 2 — Upper bound on s
There is no (91, 100)-sequence in base 2, because
- net from sequence [i] would yield (91, m, 101)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (91, 698, 101)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2698, 101, S2, 7, 607), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 478783 273124 934175 698544 745200 623223 759458 419924 748381 944798 124239 171372 376485 232113 072285 094569 060630 698755 397113 242047 437874 961827 799962 025352 795345 047866 970614 657028 403522 490871 327252 188161 782826 688095 191040 / 19 > 2698 [i]
- extracting embedded OOA [i] would yield OOA(2698, 101, S2, 7, 607), but
- m-reduction [i] would yield (91, 698, 101)-net in base 2, but