Best Known (82−77, 82, s)-Nets in Base 64
(82−77, 82, 128)-Net over F64 — Constructive and digital
Digital (5, 82, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
(82−77, 82, 133)-Net over F64 — Digital
Digital (5, 82, 133)-net over F64, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 133, using
(82−77, 82, 1502)-Net in Base 64 — Upper bound on s
There is no (5, 82, 1503)-net in base 64, because
- 31 times m-reduction [i] would yield (5, 51, 1503)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 131 077510 839072 649489 575317 954450 491451 271836 274122 635116 702982 235846 088730 419042 177697 923400 > 6451 [i]