Best Known (234−125, 234, s)-Nets in Base 2
(234−125, 234, 56)-Net over F2 — Constructive and digital
Digital (109, 234, 56)-net over F2, using
- t-expansion [i] based on digital (105, 234, 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
(234−125, 234, 65)-Net over F2 — Digital
Digital (109, 234, 65)-net over F2, using
- t-expansion [i] based on digital (95, 234, 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
(234−125, 234, 229)-Net in Base 2 — Upper bound on s
There is no (109, 234, 230)-net in base 2, because
- 17 times m-reduction [i] would yield (109, 217, 230)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2217, 230, S2, 108), but
- the linear programming bound shows that M ≥ 26 959946 667150 639794 667015 087019 630673 637144 422540 572481 103610 249216 / 93 > 2217 [i]
- extracting embedded orthogonal array [i] would yield OA(2217, 230, S2, 108), but