Best Known (162, 162+84, s)-Nets in Base 4
(162, 162+84, 200)-Net over F4 — Constructive and digital
Digital (162, 246, 200)-net over F4, using
- t-expansion [i] based on digital (161, 246, 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
(162, 162+84, 240)-Net in Base 4 — Constructive
(162, 246, 240)-net in base 4, using
- t-expansion [i] based on (161, 246, 240)-net in base 4, using
- 4 times m-reduction [i] based on (161, 250, 240)-net in base 4, using
- trace code for nets [i] based on (36, 125, 120)-net in base 16, using
- base change [i] based on digital (11, 100, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 100, 120)-net over F32, using
- trace code for nets [i] based on (36, 125, 120)-net in base 16, using
- 4 times m-reduction [i] based on (161, 250, 240)-net in base 4, using
(162, 162+84, 606)-Net over F4 — Digital
Digital (162, 246, 606)-net over F4, using
(162, 162+84, 18459)-Net in Base 4 — Upper bound on s
There is no (162, 246, 18460)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12799 091918 503718 235255 202061 772332 112413 633858 456063 672228 876789 334834 173437 732382 649566 775674 852850 708393 401841 740419 112222 308639 294955 607568 638784 > 4246 [i]