Best Known (130, 130+122, s)-Nets in Base 4
(130, 130+122, 130)-Net over F4 — Constructive and digital
Digital (130, 252, 130)-net over F4, using
- t-expansion [i] based on digital (105, 252, 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
(130, 130+122, 195)-Net over F4 — Digital
Digital (130, 252, 195)-net over F4, using
(130, 130+122, 2361)-Net in Base 4 — Upper bound on s
There is no (130, 252, 2362)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 52 869872 553372 102358 402480 164257 463079 052784 978932 155783 550711 503368 822088 019003 248733 263657 543665 486275 085929 657677 270363 172967 209649 959566 711277 039296 > 4252 [i]