Best Known (116−68, 116, s)-Nets in Base 4
(116−68, 116, 56)-Net over F4 — Constructive and digital
Digital (48, 116, 56)-net over F4, using
- t-expansion [i] based on digital (33, 116, 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
(116−68, 116, 81)-Net over F4 — Digital
Digital (48, 116, 81)-net over F4, using
- t-expansion [i] based on digital (46, 116, 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
(116−68, 116, 483)-Net in Base 4 — Upper bound on s
There is no (48, 116, 484)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7014 570615 715934 854177 063507 246132 354222 460432 403789 034813 355774 939593 > 4116 [i]