Best Known (229−115, 229, s)-Nets in Base 2
(229−115, 229, 57)-Net over F2 — Constructive and digital
Digital (114, 229, 57)-net over F2, using
- t-expansion [i] based on digital (110, 229, 57)-net over F2, using
- net from sequence [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]
- net from sequence [i] based on digital (110, 56)-sequence over F2, using
(229−115, 229, 73)-Net over F2 — Digital
Digital (114, 229, 73)-net over F2, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 114 and N(F) ≥ 73, using
(229−115, 229, 240)-Net in Base 2 — Upper bound on s
There is no (114, 229, 241)-net in base 2, because
- 7 times m-reduction [i] would yield (114, 222, 241)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2222, 241, S2, 108), but
- the linear programming bound shows that M ≥ 65 939284 597237 046425 151657 508194 701172 717895 120115 873148 022756 434178 473984 / 7 611275 > 2222 [i]
- extracting embedded orthogonal array [i] would yield OA(2222, 241, S2, 108), but