Best Known (176−71, 176, s)-Nets in Base 4
(176−71, 176, 130)-Net over F4 — Constructive and digital
Digital (105, 176, 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
(176−71, 176, 254)-Net over F4 — Digital
Digital (105, 176, 254)-net over F4, using
(176−71, 176, 4718)-Net in Base 4 — Upper bound on s
There is no (105, 176, 4719)-net in base 4, because
- 1 times m-reduction [i] would yield (105, 175, 4719)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2299 359665 513565 840296 474032 532984 630198 096022 603702 752060 688986 021993 743850 888728 703520 739423 242251 492920 > 4175 [i]