Best Known (127, 127+118, s)-Nets in Base 4
(127, 127+118, 130)-Net over F4 — Constructive and digital
Digital (127, 245, 130)-net over F4, using
- t-expansion [i] based on digital (105, 245, 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
(127, 127+118, 194)-Net over F4 — Digital
Digital (127, 245, 194)-net over F4, using
(127, 127+118, 2357)-Net in Base 4 — Upper bound on s
There is no (127, 245, 2358)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3218 903641 089725 361669 031976 695164 754179 578978 900169 598962 396079 678897 772344 052162 354910 188827 741419 509065 840499 475302 066590 719060 100308 011403 927232 > 4245 [i]