Best Known (115−68, 115, s)-Nets in Base 2
(115−68, 115, 34)-Net over F2 — Constructive and digital
Digital (47, 115, 34)-net over F2, using
- t-expansion [i] based on digital (45, 115, 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
(115−68, 115, 36)-Net over F2 — Digital
Digital (47, 115, 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
(115−68, 115, 97)-Net in Base 2 — Upper bound on s
There is no (47, 115, 98)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 46024 083362 550647 760875 176283 557080 > 2115 [i]