Best Known (210−79, 210, s)-Nets in Base 2
(210−79, 210, 70)-Net over F2 — Constructive and digital
Digital (131, 210, 70)-net over F2, using
- 1 times m-reduction [i] based on digital (131, 211, 70)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 61, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- digital (70, 150, 49)-net over F2, using
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, and 1 place with degree 2 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
- digital (21, 61, 21)-net over F2, using
- (u, u+v)-construction [i] based on
(210−79, 210, 72)-Net in Base 2 — Constructive
(131, 210, 72)-net in base 2, using
- trace code for nets [i] based on (26, 105, 36)-net in base 4, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- t-expansion [i] based on digital (51, 35)-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 3 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]
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
(210−79, 210, 111)-Net over F2 — Digital
Digital (131, 210, 111)-net over F2, using
(210−79, 210, 576)-Net in Base 2 — Upper bound on s
There is no (131, 210, 577)-net in base 2, because
- 1 times m-reduction [i] would yield (131, 209, 577)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 864 316669 434247 267539 223233 475667 961385 225652 745567 277460 732160 > 2209 [i]