Best Known (258−64, 258, s)-Nets in Base 4
(258−64, 258, 1028)-Net over F4 — Constructive and digital
Digital (194, 258, 1028)-net over F4, using
- 42 times duplication [i] based on digital (192, 256, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 64, 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, 64, 257)-net over F256, using
(258−64, 258, 2398)-Net over F4 — Digital
Digital (194, 258, 2398)-net over F4, using
(258−64, 258, 304670)-Net in Base 4 — Upper bound on s
There is no (194, 258, 304671)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 214534 760712 343653 880191 690172 464714 077463 979756 881450 007972 563698 780443 207533 742186 088380 919861 002240 798094 424674 245797 469258 618199 068507 416553 102198 826032 > 4258 [i]