Best Known (50, 50+46, s)-Nets in Base 4
(50, 50+46, 66)-Net over F4 — Constructive and digital
Digital (50, 96, 66)-net over F4, using
- t-expansion [i] based on digital (49, 96, 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
(50, 50+46, 91)-Net over F4 — Digital
Digital (50, 96, 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
(50, 50+46, 1005)-Net in Base 4 — Upper bound on s
There is no (50, 96, 1006)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 6359 560562 786721 366855 639014 696569 191377 137738 727951 266936 > 496 [i]