Best Known (48, 141, s)-Nets in Base 4
(48, 141, 56)-Net over F4 — Constructive and digital
Digital (48, 141, 56)-net over F4, using
- t-expansion [i] based on digital (33, 141, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 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) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
(48, 141, 81)-Net over F4 — Digital
Digital (48, 141, 81)-net over F4, using
- t-expansion [i] based on digital (46, 141, 81)-net over F4, using
- net from sequence [i] based on digital (46, 80)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 46 and N(F) ≥ 81, using
- net from sequence [i] based on digital (46, 80)-sequence over F4, using
(48, 141, 371)-Net in Base 4 — Upper bound on s
There is no (48, 141, 372)-net in base 4, because
- 1 times m-reduction [i] would yield (48, 140, 372)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2 110897 513405 382864 303680 369586 092724 604873 914724 910713 134682 580294 437326 270808 976012 > 4140 [i]