Best Known (165, 165+92, s)-Nets in Base 4
(165, 165+92, 200)-Net over F4 — Constructive and digital
Digital (165, 257, 200)-net over F4, using
- t-expansion [i] based on digital (161, 257, 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+92, 208)-Net in Base 4 — Constructive
(165, 257, 208)-net in base 4, using
- 3 times m-reduction [i] based on (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
- trace code for nets [i] based on (35, 130, 104)-net in base 16, using
(165, 165+92, 533)-Net over F4 — Digital
Digital (165, 257, 533)-net over F4, using
(165, 165+92, 13823)-Net in Base 4 — Upper bound on s
There is no (165, 257, 13824)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 53790 065245 911087 731480 320681 919029 431458 161992 843810 262654 584432 478402 794136 922877 222197 862824 401727 903893 782935 686420 934824 549269 234669 886594 994024 134705 > 4257 [i]