Best Known (98, 98+156, s)-Nets in Base 4
(98, 98+156, 104)-Net over F4 — Constructive and digital
Digital (98, 254, 104)-net over F4, using
- t-expansion [i] based on digital (73, 254, 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
(98, 98+156, 144)-Net over F4 — Digital
Digital (98, 254, 144)-net over F4, using
- t-expansion [i] based on digital (91, 254, 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
(98, 98+156, 846)-Net in Base 4 — Upper bound on s
There is no (98, 254, 847)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 911 816507 192724 830761 824676 465725 198671 715205 027318 151397 918762 713162 104771 809327 614757 944154 916039 073904 334104 352723 436485 027726 642530 812884 995457 335421 > 4254 [i]