Best Known (121, s)-Sequences in Base 2
(121, 56)-Sequence over F2 — Constructive and digital
Digital (121, 56)-sequence over F2, using
- t-expansion [i] based on digital (110, 56)-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 8 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]
(121, 79)-Sequence over F2 — Digital
Digital (121, 79)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 121 and N(F) ≥ 80, using
(121, 130)-Sequence in Base 2 — Upper bound on s
There is no (121, 131)-sequence in base 2, because
- net from sequence [i] would yield (121, m, 132)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (121, 914, 132)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2914, 132, S2, 7, 793), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 68 690663 818733 803848 534729 246269 043332 441249 864460 867987 169217 525115 848141 867720 454782 572015 197346 908276 916202 151748 783236 879322 844582 910748 594623 825213 660894 739770 969556 653637 026665 665005 489949 848376 317699 096431 416422 441472 432438 631162 147448 671461 006065 306468 424888 398553 022464 / 397 > 2914 [i]
- extracting embedded OOA [i] would yield OOA(2914, 132, S2, 7, 793), but
- m-reduction [i] would yield (121, 914, 132)-net in base 2, but