Best Known (130, 130+126, s)-Nets in Base 4
(130, 130+126, 130)-Net over F4 — Constructive and digital
Digital (130, 256, 130)-net over F4, using
- t-expansion [i] based on digital (105, 256, 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+126, 188)-Net over F4 — Digital
Digital (130, 256, 188)-net over F4, using
(130, 130+126, 2213)-Net in Base 4 — Upper bound on s
There is no (130, 256, 2214)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 13719 431583 492515 698518 659313 804536 555752 898397 698056 479471 183086 417182 026513 525103 069481 791622 095797 565469 403065 204481 230045 809724 664020 988814 891601 227840 > 4256 [i]