Best Known (54, 54+21, s)-Nets in Base 4
(54, 54+21, 312)-Net over F4 — Constructive and digital
Digital (54, 75, 312)-net over F4, using
- t-expansion [i] based on digital (53, 75, 312)-net over F4, using
- trace code for nets [i] based on digital (3, 25, 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
- trace code for nets [i] based on digital (3, 25, 104)-net over F64, using
(54, 54+21, 387)-Net in Base 4 — Constructive
(54, 75, 387)-net in base 4, using
- trace code for nets [i] based on (4, 25, 129)-net in base 64, using
- 3 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
- base change [i] based on digital (0, 24, 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, 24, 129)-net over F128, using
- 3 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
(54, 54+21, 511)-Net over F4 — Digital
Digital (54, 75, 511)-net over F4, using
(54, 54+21, 43054)-Net in Base 4 — Upper bound on s
There is no (54, 75, 43055)-net in base 4, because
- 1 times m-reduction [i] would yield (54, 74, 43055)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 356 841591 458623 587182 124685 691703 075885 549181 > 474 [i]