Best Known (129, 129+124, s)-Nets in Base 4
(129, 129+124, 130)-Net over F4 — Constructive and digital
Digital (129, 253, 130)-net over F4, using
- t-expansion [i] based on digital (105, 253, 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
(129, 129+124, 189)-Net over F4 — Digital
Digital (129, 253, 189)-net over F4, using
(129, 129+124, 2233)-Net in Base 4 — Upper bound on s
There is no (129, 253, 2234)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 214 501921 642657 005650 127689 906647 908145 994320 085899 333332 735424 672194 340118 912617 712081 764446 201642 428709 359590 611455 087972 877829 656890 279229 733037 523520 > 4253 [i]