Best Known (129, 129+126, s)-Nets in Base 4
(129, 129+126, 130)-Net over F4 — Constructive and digital
Digital (129, 255, 130)-net over F4, using
- t-expansion [i] based on digital (105, 255, 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+126, 185)-Net over F4 — Digital
Digital (129, 255, 185)-net over F4, using
(129, 129+126, 2163)-Net in Base 4 — Upper bound on s
There is no (129, 255, 2164)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3362 094592 733863 289161 050187 577428 362490 474291 725433 150923 640304 674923 858444 113265 144611 585665 984429 534077 212701 569834 195260 029610 447651 804686 942396 957840 > 4255 [i]