Best Known (124−77, 124, s)-Nets in Base 2
(124−77, 124, 34)-Net over F2 — Constructive and digital
Digital (47, 124, 34)-net over F2, using
- t-expansion [i] based on digital (45, 124, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-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 1 place 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 (45, 33)-sequence over F2, using
(124−77, 124, 36)-Net over F2 — Digital
Digital (47, 124, 36)-net over F2, using
- net from sequence [i] based on digital (47, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 47 and N(F) ≥ 36, using
(124−77, 124, 93)-Net in Base 2 — Upper bound on s
There is no (47, 124, 94)-net in base 2, because
- 1 times m-reduction [i] would yield (47, 123, 94)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 11 688937 235469 429023 657750 317347 637800 > 2123 [i]