Best Known (129−63, 129, s)-Nets in Base 2
(129−63, 129, 43)-Net over F2 — Constructive and digital
Digital (66, 129, 43)-net over F2, using
- t-expansion [i] based on digital (59, 129, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(129−63, 129, 48)-Net over F2 — Digital
Digital (66, 129, 48)-net over F2, using
- t-expansion [i] based on digital (65, 129, 48)-net over F2, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 65 and N(F) ≥ 48, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
(129−63, 129, 145)-Net in Base 2 — Upper bound on s
There is no (66, 129, 146)-net in base 2, because
- 1 times m-reduction [i] would yield (66, 128, 146)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2128, 146, S2, 62), but
- the linear programming bound shows that M ≥ 10 546031 115613 724859 656905 833525 360409 444352 / 30229 > 2128 [i]
- extracting embedded orthogonal array [i] would yield OA(2128, 146, S2, 62), but