Best Known (257−141, 257, s)-Nets in Base 2
(257−141, 257, 57)-Net over F2 — Constructive and digital
Digital (116, 257, 57)-net over F2, using
- t-expansion [i] based on digital (110, 257, 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
(257−141, 257, 73)-Net over F2 — Digital
Digital (116, 257, 73)-net over F2, using
- t-expansion [i] based on digital (114, 257, 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
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
(257−141, 257, 244)-Net in Base 2 — Upper bound on s
There is no (116, 257, 245)-net in base 2, because
- 33 times m-reduction [i] would yield (116, 224, 245)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2224, 245, S2, 108), but
- the linear programming bound shows that M ≥ 227 481559 590216 982433 849553 220650 758912 788551 722735 940858 156798 416424 796160 / 8 133191 > 2224 [i]
- extracting embedded orthogonal array [i] would yield OA(2224, 245, S2, 108), but