Best Known (257−124, 257, s)-Nets in Base 4
(257−124, 257, 130)-Net over F4 — Constructive and digital
Digital (133, 257, 130)-net over F4, using
- t-expansion [i] based on digital (105, 257, 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
(257−124, 257, 201)-Net over F4 — Digital
Digital (133, 257, 201)-net over F4, using
(257−124, 257, 2446)-Net in Base 4 — Upper bound on s
There is no (133, 257, 2447)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 53935 939038 511513 123053 126653 366342 384727 936970 239348 972010 181375 317541 490464 521187 360037 880354 998083 815161 478557 134720 764429 658130 181116 417754 476011 874280 > 4257 [i]