Best Known (83−50, 83, s)-Nets in Base 4
(83−50, 83, 56)-Net over F4 — Constructive and digital
Digital (33, 83, 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
(83−50, 83, 65)-Net over F4 — Digital
Digital (33, 83, 65)-net over F4, using
- net from sequence [i] based on digital (33, 64)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 65, using
(83−50, 83, 318)-Net in Base 4 — Upper bound on s
There is no (33, 83, 319)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 97 374421 967468 796673 880271 749565 307359 005596 936990 > 483 [i]