Best Known (6, 6+37, s)-Nets in Base 64
(6, 6+37, 128)-Net over F64 — Constructive and digital
Digital (6, 43, 128)-net over F64, using
- t-expansion [i] based on digital (5, 43, 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+37, 161)-Net over F64 — Digital
Digital (6, 43, 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+37, 1955)-Net in Base 64 — Upper bound on s
There is no (6, 43, 1956)-net in base 64, because
- 1 times m-reduction [i] would yield (6, 42, 1956)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 7268 253839 045773 987658 216937 652645 408160 936325 936390 832875 410330 639708 415802 > 6442 [i]