Best Known (100, ∞, s)-Nets in Base 2
(100, ∞, 55)-Net over F2 — Constructive and digital
Digital (100, m, 55)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (100, 54)-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 6 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]
(100, ∞, 65)-Net over F2 — Digital
Digital (100, m, 65)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (100, 64)-sequence over F2, using
- t-expansion [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- t-expansion [i] based on digital (95, 64)-sequence over F2, using
(100, ∞, 109)-Net in Base 2 — Upper bound on s
There is no (100, m, 110)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (100, 871, 110)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2871, 110, S2, 8, 771), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 164625 190444 848374 033579 133993 978438 087949 530281 437216 631177 142690 463495 668819 449971 850765 747400 962317 870658 446689 929498 891587 837339 633494 238803 823919 619767 623714 312428 236660 895199 628262 570937 027271 712259 961630 977206 042016 835925 266340 904732 113311 641645 349704 040448 / 193 > 2871 [i]
- extracting embedded OOA [i] would yield OOA(2871, 110, S2, 8, 771), but