Best Known (159, 212, s)-Nets in Base 4
(159, 212, 1028)-Net over F4 — Constructive and digital
Digital (159, 212, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 53, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
(159, 212, 1946)-Net over F4 — Digital
Digital (159, 212, 1946)-net over F4, using
(159, 212, 270449)-Net in Base 4 — Upper bound on s
There is no (159, 212, 270450)-net in base 4, because
- 1 times m-reduction [i] would yield (159, 211, 270450)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10 831258 032547 057709 431726 823107 287706 583690 070778 542537 662266 499137 755069 673715 827065 562496 864959 751265 493820 365569 211843 325200 > 4211 [i]