Best Known (94, 94+43, s)-Nets in Base 2
(94, 94+43, 69)-Net over F2 — Constructive and digital
Digital (94, 137, 69)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (0, 21, 3)-net over F2, using
- net from sequence [i] based on digital (0, 2)-sequence over F2, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 0 and N(F) ≥ 3, using
- the rational function field F2(x) [i]
- Niederreiter sequence [i]
- Sobol sequence [i]
- net from sequence [i] based on digital (0, 2)-sequence over F2, using
- digital (73, 116, 66)-net over F2, using
- trace code for nets [i] based on digital (15, 58, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- trace code for nets [i] based on digital (15, 58, 33)-net over F4, using
- digital (0, 21, 3)-net over F2, using
(94, 94+43, 70)-Net in Base 2 — Constructive
(94, 137, 70)-net in base 2, using
- 3 times m-reduction [i] based on (94, 140, 70)-net in base 2, using
- trace code for nets [i] based on (24, 70, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- base expansion [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]
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- trace code for nets [i] based on (24, 70, 35)-net in base 4, using
(94, 94+43, 118)-Net over F2 — Digital
Digital (94, 137, 118)-net over F2, using
(94, 94+43, 742)-Net in Base 2 — Upper bound on s
There is no (94, 137, 743)-net in base 2, because
- 1 times m-reduction [i] would yield (94, 136, 743)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 88856 125161 162278 039008 177811 509277 654328 > 2136 [i]