Best Known (18, 18+42, s)-Nets in Base 2
(18, 18+42, 17)-Net over F2 — Constructive and digital
Digital (18, 60, 17)-net over F2, using
- t-expansion [i] based on digital (15, 60, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
(18, 18+42, 18)-Net over F2 — Digital
Digital (18, 60, 18)-net over F2, using
- net from sequence [i] based on digital (18, 17)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 18 and N(F) ≥ 18, using
(18, 18+42, 31)-Net in Base 2 — Upper bound on s
There is no (18, 60, 32)-net in base 2, because
- 3 times m-reduction [i] would yield (18, 57, 32)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(257, 32, S2, 2, 39), but
- the LP bound with quadratic polynomials shows that M ≥ 792633 534417 207296 / 5 > 257 [i]
- extracting embedded OOA [i] would yield OOA(257, 32, S2, 2, 39), but