Best Known (45−27, 45, s)-Nets in Base 2
(45−27, 45, 17)-Net over F2 — Constructive and digital
Digital (18, 45, 17)-net over F2, using
- t-expansion [i] based on digital (15, 45, 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
(45−27, 45, 18)-Net over F2 — Digital
Digital (18, 45, 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
(45−27, 45, 42)-Net in Base 2 — Upper bound on s
There is no (18, 45, 43)-net in base 2, because
- 1 times m-reduction [i] would yield (18, 44, 43)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 19 417026 669552 > 244 [i]