Best Known (6, 6+36, s)-Nets in Base 64
(6, 6+36, 128)-Net over F64 — Constructive and digital
Digital (6, 42, 128)-net over F64, using
- t-expansion [i] based on digital (5, 42, 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+36, 129)-Net in Base 64 — Constructive
(6, 42, 129)-net in base 64, using
- base change [i] based on digital (0, 36, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
(6, 6+36, 161)-Net over F64 — Digital
Digital (6, 42, 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+36, 1955)-Net in Base 64 — Upper bound on s
There is no (6, 42, 1956)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 7268 253839 045773 987658 216937 652645 408160 936325 936390 832875 410330 639708 415802 > 6442 [i]