Best Known (6, 6+79, s)-Nets in Base 64
(6, 6+79, 128)-Net over F64 — Constructive and digital
Digital (6, 85, 128)-net over F64, using
- t-expansion [i] based on digital (5, 85, 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
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
(6, 6+79, 161)-Net over F64 — Digital
Digital (6, 85, 161)-net over F64, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 6 and N(F) ≥ 161, using
(6, 6+79, 1776)-Net in Base 64 — Upper bound on s
There is no (6, 85, 1777)-net in base 64, because
- 23 times m-reduction [i] would yield (6, 62, 1777)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 9628 243677 332979 985102 055123 697968 863615 149142 257563 526399 934787 098909 501690 444032 902233 177985 774325 020091 801976 > 6462 [i]