Best Known (234−136, 234, s)-Nets in Base 4
(234−136, 234, 104)-Net over F4 — Constructive and digital
Digital (98, 234, 104)-net over F4, using
- t-expansion [i] based on digital (73, 234, 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
(234−136, 234, 144)-Net over F4 — Digital
Digital (98, 234, 144)-net over F4, using
- t-expansion [i] based on digital (91, 234, 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
(234−136, 234, 973)-Net in Base 4 — Upper bound on s
There is no (98, 234, 974)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 784 986915 554899 651411 397019 857252 651738 638470 991637 084450 326574 351254 753478 818328 766530 503182 842096 923904 830648 121329 294310 399526 714674 793625 > 4234 [i]