Best Known (46−41, 46, s)-Nets in Base 64
(46−41, 46, 128)-Net over F64 — Constructive and digital
Digital (5, 46, 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
(46−41, 46, 133)-Net over F64 — Digital
Digital (5, 46, 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
(46−41, 46, 1517)-Net in Base 64 — Upper bound on s
There is no (5, 46, 1518)-net in base 64, because
- 1 times m-reduction [i] would yield (5, 45, 1518)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 1914 443406 102487 863522 121076 237909 969863 001309 460459 184060 626521 641096 594926 317314 > 6445 [i]