Best Known (59, 181, s)-Nets in Base 4
(59, 181, 66)-Net over F4 — Constructive and digital
Digital (59, 181, 66)-net over F4, using
- t-expansion [i] based on digital (49, 181, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second 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) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(59, 181, 91)-Net over F4 — Digital
Digital (59, 181, 91)-net over F4, using
- t-expansion [i] based on digital (50, 181, 91)-net over F4, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
(59, 181, 431)-Net in Base 4 — Upper bound on s
There is no (59, 181, 432)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 9 504564 365167 315544 075011 099571 926667 101410 085560 633188 572437 046235 784912 763677 142435 909409 131177 295090 001880 > 4181 [i]