Best Known (87−54, 87, s)-Nets in Base 2
(87−54, 87, 24)-Net over F2 — Constructive and digital
Digital (33, 87, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
(87−54, 87, 28)-Net over F2 — Digital
Digital (33, 87, 28)-net over F2, using
- net from sequence [i] based on digital (33, 27)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 28, using
(87−54, 87, 67)-Net in Base 2 — Upper bound on s
There is no (33, 87, 68)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 159 140444 509566 663495 081112 > 287 [i]