Best Known (251−204, 251, s)-Nets in Base 2
(251−204, 251, 34)-Net over F2 — Constructive and digital
Digital (47, 251, 34)-net over F2, using
- t-expansion [i] based on digital (45, 251, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
(251−204, 251, 36)-Net over F2 — Digital
Digital (47, 251, 36)-net over F2, using
- net from sequence [i] based on digital (47, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 47 and N(F) ≥ 36, using
(251−204, 251, 58)-Net in Base 2 — Upper bound on s
There is no (47, 251, 59)-net in base 2, because
- 25 times m-reduction [i] would yield (47, 226, 59)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2226, 59, S2, 4, 179), but
- the LP bound with quadratic polynomials shows that M ≥ 5445 909226 764429 238522 737047 577965 396074 703173 353195 641182 929270 341632 / 45 > 2226 [i]
- extracting embedded OOA [i] would yield OOA(2226, 59, S2, 4, 179), but