Best Known (125, 125+114, s)-Nets in Base 4
(125, 125+114, 130)-Net over F4 — Constructive and digital
Digital (125, 239, 130)-net over F4, using
- t-expansion [i] based on digital (105, 239, 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
(125, 125+114, 195)-Net over F4 — Digital
Digital (125, 239, 195)-net over F4, using
(125, 125+114, 2415)-Net in Base 4 — Upper bound on s
There is no (125, 239, 2416)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 791092 312062 042218 901636 590448 298781 023879 823516 125402 302948 644722 944144 400971 294752 872007 454078 788872 662472 053951 089202 990968 391178 648031 242060 > 4239 [i]