Best Known (165, 165+95, s)-Nets in Base 4
(165, 165+95, 200)-Net over F4 — Constructive and digital
Digital (165, 260, 200)-net over F4, using
- t-expansion [i] based on digital (161, 260, 200)-net over F4, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 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) = 161 and N(F) ≥ 200, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
(165, 165+95, 208)-Net in Base 4 — Constructive
(165, 260, 208)-net in base 4, using
- trace code for nets [i] based on (35, 130, 104)-net in base 16, using
- base change [i] based on digital (9, 104, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 104, 104)-net over F32, using
(165, 165+95, 501)-Net over F4 — Digital
Digital (165, 260, 501)-net over F4, using
(165, 165+95, 12687)-Net in Base 4 — Upper bound on s
There is no (165, 260, 12688)-net in base 4, because
- 1 times m-reduction [i] would yield (165, 259, 12688)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 858121 644802 042442 829284 037195 008367 710832 832076 672774 817818 116309 808353 189503 035844 321326 765275 559396 317674 348919 480138 402882 311681 269539 605840 283998 661180 > 4259 [i]