Best Known (196−103, 196, s)-Nets in Base 4
(196−103, 196, 104)-Net over F4 — Constructive and digital
Digital (93, 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
(196−103, 196, 144)-Net over F4 — Digital
Digital (93, 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
(196−103, 196, 1285)-Net in Base 4 — Upper bound on s
There is no (93, 196, 1286)-net in base 4, because
- 1 times m-reduction [i] would yield (93, 195, 1286)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2613 968334 115517 438214 166022 535099 076240 139138 879001 036544 136356 485894 205354 857340 222638 354061 810572 242800 235516 295520 > 4195 [i]