Best Known (146, 146+109, s)-Nets in Base 2
(146, 146+109, 70)-Net over F2 — Constructive and digital
Digital (146, 255, 70)-net over F2, using
- 1 times m-reduction [i] based on digital (146, 256, 70)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 76, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- digital (70, 180, 49)-net over F2, using
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, and 1 place with degree 2 [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 (70, 48)-sequence over F2, using
- digital (21, 76, 21)-net over F2, using
- (u, u+v)-construction [i] based on
(146, 146+109, 98)-Net over F2 — Digital
Digital (146, 255, 98)-net over F2, using
(146, 146+109, 470)-Net in Base 2 — Upper bound on s
There is no (146, 255, 471)-net in base 2, because
- 1 times m-reduction [i] would yield (146, 254, 471)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 29204 624772 146489 935573 989907 894869 057136 281872 765569 270908 345644 379638 002774 > 2254 [i]