Best Known (50, 50+56, s)-Nets in Base 4
(50, 50+56, 66)-Net over F4 — Constructive and digital
Digital (50, 106, 66)-net over F4, using
- t-expansion [i] based on digital (49, 106, 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+56, 91)-Net over F4 — Digital
Digital (50, 106, 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+56, 693)-Net in Base 4 — Upper bound on s
There is no (50, 106, 694)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 6641 880382 345137 211553 254921 770197 661674 665963 805215 299061 118020 > 4106 [i]