Best Known (73−65, 73, s)-Nets in Base 128
(73−65, 73, 216)-Net over F128 — Constructive and digital
Digital (8, 73, 216)-net over F128, using
- t-expansion [i] based on digital (5, 73, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
(73−65, 73, 276)-Net over F128 — Digital
Digital (8, 73, 276)-net over F128, using
- net from sequence [i] based on digital (8, 275)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 8 and N(F) ≥ 276, using
(73−65, 73, 5534)-Net in Base 128 — Upper bound on s
There is no (8, 73, 5535)-net in base 128, because
- 1 times m-reduction [i] would yield (8, 72, 5535)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 52 575645 895891 750265 842143 819908 526309 607974 144529 099621 522780 501019 674349 612382 329612 113486 312641 770495 188053 943191 062320 520754 305787 104065 213776 799820 > 12872 [i]