Best Known (237−134, 237, s)-Nets in Base 4
(237−134, 237, 104)-Net over F4 — Constructive and digital
Digital (103, 237, 104)-net over F4, using
- t-expansion [i] based on digital (73, 237, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(237−134, 237, 144)-Net over F4 — Digital
Digital (103, 237, 144)-net over F4, using
- t-expansion [i] based on digital (91, 237, 144)-net over F4, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 91 and N(F) ≥ 144, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
(237−134, 237, 1104)-Net in Base 4 — Upper bound on s
There is no (103, 237, 1105)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 50996 798284 279660 778738 237378 170071 172036 033225 756970 129435 618167 333741 959157 751287 743781 535596 822903 181336 871596 622947 103563 542753 577058 532144 > 4237 [i]