Best Known (98, 98+98, s)-Nets in Base 4
(98, 98+98, 104)-Net over F4 — Constructive and digital
Digital (98, 196, 104)-net over F4, using
- t-expansion [i] based on digital (73, 196, 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+98, 144)-Net over F4 — Digital
Digital (98, 196, 144)-net over F4, using
- t-expansion [i] based on digital (91, 196, 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+98, 1590)-Net in Base 4 — Upper bound on s
There is no (98, 196, 1591)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 10104 480335 037255 531789 430942 775037 560037 619693 508081 299146 942079 781179 823326 913590 878114 055162 437498 006305 720724 864382 > 4196 [i]