Best Known (254−88, 254, s)-Nets in Base 4
(254−88, 254, 200)-Net over F4 — Constructive and digital
Digital (166, 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
(254−88, 254, 240)-Net in Base 4 — Constructive
(166, 254, 240)-net in base 4, using
- 4 times m-reduction [i] based on (166, 258, 240)-net in base 4, using
- trace code for nets [i] based on (37, 129, 120)-net in base 16, using
- 1 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
- base change [i] based on digital (11, 104, 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, 104, 120)-net over F32, using
- 1 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
- trace code for nets [i] based on (37, 129, 120)-net in base 16, using
(254−88, 254, 592)-Net over F4 — Digital
Digital (166, 254, 592)-net over F4, using
(254−88, 254, 17155)-Net in Base 4 — Upper bound on s
There is no (166, 254, 17156)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 838 012431 516407 560707 551356 504780 794270 733351 440708 274469 522499 458038 785073 948350 869109 475615 895118 296419 363137 020795 064981 565315 310522 561343 628770 031936 > 4254 [i]