Best Known (212−105, 212, s)-Nets in Base 2
(212−105, 212, 56)-Net over F2 — Constructive and digital
Digital (107, 212, 56)-net over F2, using
- t-expansion [i] based on digital (105, 212, 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
(212−105, 212, 65)-Net over F2 — Digital
Digital (107, 212, 65)-net over F2, using
- t-expansion [i] based on digital (95, 212, 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
(212−105, 212, 226)-Net in Base 2 — Upper bound on s
There is no (107, 212, 227)-net in base 2, because
- 5 times m-reduction [i] would yield (107, 207, 227)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2207, 227, S2, 100), but
- the linear programming bound shows that M ≥ 1 579684 375028 357800 468770 415255 056484 783426 431008 236668 814664 663040 / 6409 > 2207 [i]
- extracting embedded orthogonal array [i] would yield OA(2207, 227, S2, 100), but