Best Known (87−37, 87, s)-Nets in Base 2
(87−37, 87, 35)-Net over F2 — Constructive and digital
Digital (50, 87, 35)-net over F2, using
- t-expansion [i] based on digital (48, 87, 35)-net over F2, using
- net from sequence [i] based on digital (48, 34)-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 2 places 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 (48, 34)-sequence over F2, using
(87−37, 87, 42)-Net over F2 — Digital
Digital (50, 87, 42)-net over F2, using
(87−37, 87, 182)-Net in Base 2 — Upper bound on s
There is no (50, 87, 183)-net in base 2, because
- 1 times m-reduction [i] would yield (50, 86, 183)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 83 419280 786025 635792 371945 > 286 [i]