Best Known (129, 129+122, s)-Nets in Base 4
(129, 129+122, 130)-Net over F4 — Constructive and digital
Digital (129, 251, 130)-net over F4, using
- t-expansion [i] based on digital (105, 251, 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+122, 192)-Net over F4 — Digital
Digital (129, 251, 192)-net over F4, using
(129, 129+122, 2307)-Net in Base 4 — Upper bound on s
There is no (129, 251, 2308)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 13 281514 005575 031118 616680 915858 207021 755221 324442 327311 419915 802768 374614 014934 004827 193060 753598 298420 101666 904360 600106 233815 533220 198959 679520 180160 > 4251 [i]