Best Known (98, 98+∞, s)-Nets in Base 2
(98, 98+∞, 54)-Net over F2 — Constructive and digital
Digital (98, m, 54)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (98, 53)-sequence over F2, using
- t-expansion [i] based on digital (95, 53)-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 5 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]
- t-expansion [i] based on digital (95, 53)-sequence over F2, using
(98, 98+∞, 65)-Net over F2 — Digital
Digital (98, m, 65)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (98, 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
(98, 98+∞, 107)-Net in Base 2 — Upper bound on s
There is no (98, m, 108)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (98, 855, 108)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2855, 108, S2, 8, 757), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 97 057177 562787 164573 067126 687543 672703 038428 025407 981722 171883 323779 300841 541427 520344 119047 246524 091610 106360 019872 220740 793824 933955 400888 052166 601040 693908 993589 655255 188519 807931 307366 871890 472698 439642 645150 923182 623169 682730 117852 928334 233518 627012 739072 / 379 > 2855 [i]
- extracting embedded OOA [i] would yield OOA(2855, 108, S2, 8, 757), but