Best Known (178−68, 178, s)-Nets in Base 4
(178−68, 178, 130)-Net over F4 — Constructive and digital
Digital (110, 178, 130)-net over F4, using
- t-expansion [i] based on digital (105, 178, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(178−68, 178, 309)-Net over F4 — Digital
Digital (110, 178, 309)-net over F4, using
(178−68, 178, 6374)-Net in Base 4 — Upper bound on s
There is no (110, 178, 6375)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 147402 846709 515519 301420 297529 218395 399560 126673 747087 016283 114792 940165 700653 743372 298846 850128 330618 428341 > 4178 [i]