Best Known (227−114, 227, s)-Nets in Base 2
(227−114, 227, 57)-Net over F2 — Constructive and digital
Digital (113, 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
(227−114, 227, 72)-Net over F2 — Digital
Digital (113, 227, 72)-net over F2, using
- t-expansion [i] based on digital (110, 227, 72)-net over F2, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 110 and N(F) ≥ 72, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
(227−114, 227, 238)-Net in Base 2 — Upper bound on s
There is no (113, 227, 239)-net in base 2, because
- 8 times m-reduction [i] would yield (113, 219, 239)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2219, 239, S2, 106), but
- the linear programming bound shows that M ≥ 241561 122137 669732 560216 455179 695890 835788 814025 963529 430688 347832 975360 / 208437 > 2219 [i]
- extracting embedded orthogonal array [i] would yield OA(2219, 239, S2, 106), but