Best Known (63−18, 63, s)-Nets in Base 4
(63−18, 63, 312)-Net over F4 — Constructive and digital
Digital (45, 63, 312)-net over F4, using
- trace code for nets [i] based on digital (3, 21, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
(63−18, 63, 387)-Net in Base 4 — Constructive
(45, 63, 387)-net in base 4, using
- trace code for nets [i] based on (3, 21, 129)-net in base 64, using
- base change [i] based on digital (0, 18, 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
- base change [i] based on digital (0, 18, 129)-net over F128, using
(63−18, 63, 416)-Net over F4 — Digital
Digital (45, 63, 416)-net over F4, using
(63−18, 63, 22642)-Net in Base 4 — Upper bound on s
There is no (45, 63, 22643)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 85 102431 652263 210660 277446 331538 346628 > 463 [i]