Best Known (253−165, 253, s)-Nets in Base 4
(253−165, 253, 104)-Net over F4 — Constructive and digital
Digital (88, 253, 104)-net over F4, using
- t-expansion [i] based on digital (73, 253, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(253−165, 253, 129)-Net over F4 — Digital
Digital (88, 253, 129)-net over F4, using
- t-expansion [i] based on digital (81, 253, 129)-net over F4, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 81 and N(F) ≥ 129, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
(253−165, 253, 674)-Net in Base 4 — Upper bound on s
There is no (88, 253, 675)-net in base 4, because
- 1 times m-reduction [i] would yield (88, 252, 675)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 56 420016 306956 154906 655281 684351 588336 332721 591449 577130 997255 720546 463747 082357 820273 335691 009140 762438 785012 926268 323575 752145 558514 523593 963978 828548 > 4252 [i]