Best Known (72−48, 72, s)-Nets in Base 128
(72−48, 72, 288)-Net over F128 — Constructive and digital
Digital (24, 72, 288)-net over F128, using
- t-expansion [i] based on digital (9, 72, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
(72−48, 72, 513)-Net over F128 — Digital
Digital (24, 72, 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
(72−48, 72, 161866)-Net in Base 128 — Upper bound on s
There is no (24, 72, 161867)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 52 376431 473613 751772 184701 005830 550632 537708 280799 168221 693690 571518 754613 857514 273825 034581 192897 560948 208670 073983 693413 773619 689112 751699 353679 453716 > 12872 [i]