Best Known (59, 82, s)-Nets in Base 4
(59, 82, 312)-Net over F4 — Constructive and digital
Digital (59, 82, 312)-net over F4, using
- 2 times m-reduction [i] based on digital (59, 84, 312)-net over F4, using
- trace code for nets [i] based on digital (3, 28, 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, 28, 104)-net over F64, using
(59, 82, 387)-Net in Base 4 — Constructive
(59, 82, 387)-net in base 4, using
- 41 times duplication [i] based on (58, 81, 387)-net in base 4, using
- trace code for nets [i] based on (4, 27, 129)-net in base 64, using
- 1 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
- 1 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
- trace code for nets [i] based on (4, 27, 129)-net in base 64, using
(59, 82, 540)-Net over F4 — Digital
Digital (59, 82, 540)-net over F4, using
(59, 82, 44377)-Net in Base 4 — Upper bound on s
There is no (59, 82, 44378)-net in base 4, because
- 1 times m-reduction [i] would yield (59, 81, 44378)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 5 847306 539445 012325 006505 038035 762313 836620 416600 > 481 [i]