Best Known (227−119, 227, s)-Nets in Base 2
(227−119, 227, 56)-Net over F2 — Constructive and digital
Digital (108, 227, 56)-net over F2, using
- t-expansion [i] based on digital (105, 227, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-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 7 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 (105, 55)-sequence over F2, using
(227−119, 227, 65)-Net over F2 — Digital
Digital (108, 227, 65)-net over F2, using
- t-expansion [i] based on digital (95, 227, 65)-net over F2, using
- net from sequence [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
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(227−119, 227, 226)-Net in Base 2 — Upper bound on s
There is no (108, 227, 227)-net in base 2, because
- 13 times m-reduction [i] would yield (108, 214, 227)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2214, 227, S2, 106), but
- the linear programming bound shows that M ≥ 458 319093 341560 876509 339256 479333 721451 831455 183189 732178 761374 236672 / 17019 > 2214 [i]
- extracting embedded orthogonal array [i] would yield OA(2214, 227, S2, 106), but