Best Known (70−44, 70, s)-Nets in Base 128
(70−44, 70, 342)-Net over F128 — Constructive and digital
Digital (26, 70, 342)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 23, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (3, 47, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (1, 23, 150)-net over F128, using
(70−44, 70, 513)-Net over F128 — Digital
Digital (26, 70, 513)-net over F128, using
- t-expansion [i] based on digital (24, 70, 513)-net over F128, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
(70−44, 70, 361239)-Net in Base 128 — Upper bound on s
There is no (26, 70, 361240)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 3196 729579 374888 765167 275459 041794 912809 004992 256313 379880 871883 000123 552093 931394 745984 956224 839236 285009 563327 229615 132924 369683 084218 105221 827399 > 12870 [i]