Best Known (126, 126+124, s)-Nets in Base 4
(126, 126+124, 130)-Net over F4 — Constructive and digital
Digital (126, 250, 130)-net over F4, using
- t-expansion [i] based on digital (105, 250, 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
(126, 126+124, 180)-Net over F4 — Digital
Digital (126, 250, 180)-net over F4, using
(126, 126+124, 2084)-Net in Base 4 — Upper bound on s
There is no (126, 250, 2085)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 274683 971121 239561 299981 803971 260535 460468 851699 482056 595283 376590 249468 573761 393630 441404 160349 273191 341088 757904 135767 269957 526307 986230 765298 590720 > 4250 [i]