Best Known (254−92, 254, s)-Nets in Base 4
(254−92, 254, 200)-Net over F4 — Constructive and digital
Digital (162, 254, 200)-net over F4, using
- t-expansion [i] based on digital (161, 254, 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
(254−92, 254, 208)-Net in Base 4 — Constructive
(162, 254, 208)-net in base 4, using
- trace code for nets [i] based on (35, 127, 104)-net in base 16, using
- 3 times m-reduction [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
- 3 times m-reduction [i] based on (35, 130, 104)-net in base 16, using
(254−92, 254, 506)-Net over F4 — Digital
Digital (162, 254, 506)-net over F4, using
(254−92, 254, 12624)-Net in Base 4 — Upper bound on s
There is no (162, 254, 12625)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 838 225405 797867 109211 305227 206032 067899 456323 586856 607624 250700 232804 144085 331892 305939 565454 406950 740487 055845 982287 448637 163767 290223 517587 873821 961616 > 4254 [i]