Best Known (100, 100+158, s)-Nets in Base 4
(100, 100+158, 104)-Net over F4 — Constructive and digital
Digital (100, 258, 104)-net over F4, using
- t-expansion [i] based on digital (73, 258, 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
(100, 100+158, 144)-Net over F4 — Digital
Digital (100, 258, 144)-net over F4, using
- t-expansion [i] based on digital (91, 258, 144)-net over F4, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 91 and N(F) ≥ 144, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
(100, 100+158, 868)-Net in Base 4 — Upper bound on s
There is no (100, 258, 869)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 223201 667845 230822 077537 865536 532676 713673 472154 824689 727830 048540 429627 982253 725903 411250 449348 141902 531438 399133 793553 563761 137382 713368 621072 261713 403424 > 4258 [i]