Best Known (98, 98+111, s)-Nets in Base 4
(98, 98+111, 104)-Net over F4 — Constructive and digital
Digital (98, 209, 104)-net over F4, using
- t-expansion [i] based on digital (73, 209, 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+111, 144)-Net over F4 — Digital
Digital (98, 209, 144)-net over F4, using
- t-expansion [i] based on digital (91, 209, 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+111, 1300)-Net in Base 4 — Upper bound on s
There is no (98, 209, 1301)-net in base 4, because
- 1 times m-reduction [i] would yield (98, 208, 1301)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 170294 774571 630203 263923 241400 931865 675717 410877 389938 579245 416979 901065 213214 915356 266020 992825 333151 123640 905626 564074 356992 > 4208 [i]