Best Known (163, 163+95, s)-Nets in Base 4
(163, 163+95, 200)-Net over F4 — Constructive and digital
Digital (163, 258, 200)-net over F4, using
- t-expansion [i] based on digital (161, 258, 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
(163, 163+95, 484)-Net over F4 — Digital
Digital (163, 258, 484)-net over F4, using
(163, 163+95, 11958)-Net in Base 4 — Upper bound on s
There is no (163, 258, 11959)-net in base 4, because
- 1 times m-reduction [i] would yield (163, 257, 11959)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 53641 337306 859488 441447 319912 514218 953612 884009 800480 729877 394181 318878 994168 648009 586459 608275 754983 155903 681332 518915 464509 359741 138537 304089 015460 678040 > 4257 [i]