Best Known (129, 129+77, s)-Nets in Base 2
(129, 129+77, 70)-Net over F2 — Constructive and digital
Digital (129, 206, 70)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 59, 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, 147, 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, 59, 21)-net over F2, using
(129, 129+77, 72)-Net in Base 2 — Constructive
(129, 206, 72)-net in base 2, using
- trace code for nets [i] based on (26, 103, 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
(129, 129+77, 110)-Net over F2 — Digital
Digital (129, 206, 110)-net over F2, using
- trace code for nets [i] based on digital (26, 103, 55)-net over F4, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 26 and N(F) ≥ 55, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
(129, 129+77, 577)-Net in Base 2 — Upper bound on s
There is no (129, 206, 578)-net in base 2, because
- 1 times m-reduction [i] would yield (129, 205, 578)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 52 058734 457457 401455 988061 852518 570379 724489 280786 270723 984160 > 2205 [i]