Best Known (137, 137+123, s)-Nets in Base 2
(137, 137+123, 63)-Net over F2 — Constructive and digital
Digital (137, 260, 63)-net over F2, using
- 21 times duplication [i] based on digital (136, 259, 63)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 82, 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 (54, 177, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- digital (21, 82, 21)-net over F2, using
- (u, u+v)-construction [i] based on
(137, 137+123, 81)-Net over F2 — Digital
Digital (137, 260, 81)-net over F2, using
- t-expansion [i] based on digital (126, 260, 81)-net over F2, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 126 and N(F) ≥ 81, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
(137, 137+123, 363)-Net in Base 2 — Upper bound on s
There is no (137, 260, 364)-net in base 2, because
- 1 times m-reduction [i] would yield (137, 259, 364)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 966245 715120 787331 154932 340518 389797 764310 950939 196375 107014 049761 159219 636400 > 2259 [i]