Best Known (229−154, 229, s)-Nets in Base 4
(229−154, 229, 104)-Net over F4 — Constructive and digital
Digital (75, 229, 104)-net over F4, using
- t-expansion [i] based on digital (73, 229, 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
(229−154, 229, 112)-Net over F4 — Digital
Digital (75, 229, 112)-net over F4, using
- t-expansion [i] based on digital (73, 229, 112)-net over F4, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 112, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
(229−154, 229, 545)-Net in Base 4 — Upper bound on s
There is no (75, 229, 546)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 786734 269105 464464 316875 188120 719515 231839 612467 031755 376363 683819 850831 364691 613245 234496 782368 409529 763776 773021 420215 671402 926365 505088 > 4229 [i]