Best Known (72−44, 72, s)-Nets in Base 128
(72−44, 72, 384)-Net over F128 — Constructive and digital
Digital (28, 72, 384)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 25, 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 (3, 47, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128 (see above)
- digital (3, 25, 192)-net over F128, using
(72−44, 72, 577)-Net over F128 — Digital
Digital (28, 72, 577)-net over F128, using
- net from sequence [i] based on digital (28, 576)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 28 and N(F) ≥ 577, using
(72−44, 72, 561519)-Net in Base 128 — Upper bound on s
There is no (28, 72, 561520)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 52 375951 068375 984229 654651 190790 272629 009444 272909 736164 232515 501124 834735 602736 460500 933427 341519 697489 291071 831733 063222 887438 982549 089453 320012 105238 > 12872 [i]