Best Known (227−107, 227, s)-Nets in Base 2
(227−107, 227, 57)-Net over F2 — Constructive and digital
Digital (120, 227, 57)-net over F2, using
- t-expansion [i] based on digital (110, 227, 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
(227−107, 227, 73)-Net over F2 — Digital
Digital (120, 227, 73)-net over F2, using
- t-expansion [i] based on digital (114, 227, 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
(227−107, 227, 256)-Net in Base 2 — Upper bound on s
There is no (120, 227, 257)-net in base 2, because
- 1 times m-reduction [i] would yield (120, 226, 257)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2226, 257, S2, 106), but
- the linear programming bound shows that M ≥ 244 189334 532657 083315 428718 753162 243643 319191 648566 414202 988087 942294 251952 406528 / 2 259726 253785 > 2226 [i]
- extracting embedded orthogonal array [i] would yield OA(2226, 257, S2, 106), but