Best Known (177−68, 177, s)-Nets in Base 4
(177−68, 177, 130)-Net over F4 — Constructive and digital
Digital (109, 177, 130)-net over F4, using
- t-expansion [i] based on digital (105, 177, 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
(177−68, 177, 301)-Net over F4 — Digital
Digital (109, 177, 301)-net over F4, using
(177−68, 177, 6118)-Net in Base 4 — Upper bound on s
There is no (109, 177, 6119)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 36812 131937 238891 906061 763512 065519 848760 205251 510102 457969 363202 369599 551373 167148 113512 903869 626777 938317 > 4177 [i]