Best Known (128, 128+42, s)-Nets in Base 4
(128, 128+42, 1028)-Net over F4 — Constructive and digital
Digital (128, 170, 1028)-net over F4, using
- 42 times duplication [i] based on digital (126, 168, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 42, 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
- trace code for nets [i] based on digital (0, 42, 257)-net over F256, using
(128, 128+42, 1707)-Net over F4 — Digital
Digital (128, 170, 1707)-net over F4, using
(128, 128+42, 216349)-Net in Base 4 — Upper bound on s
There is no (128, 170, 216350)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 239824 077510 824876 919133 914461 671684 690523 645591 647135 862852 961550 489146 598186 502735 601510 453530 207831 > 4170 [i]