Best Known (124, 124+88, s)-Nets in Base 4
(124, 124+88, 130)-Net over F4 — Constructive and digital
Digital (124, 212, 130)-net over F4, using
- t-expansion [i] based on digital (105, 212, 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
(124, 124+88, 273)-Net over F4 — Digital
Digital (124, 212, 273)-net over F4, using
(124, 124+88, 4541)-Net in Base 4 — Upper bound on s
There is no (124, 212, 4542)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 43 522247 176174 522136 761677 190410 533097 865864 683056 503223 330139 001705 180668 284984 508253 881454 905897 985371 129601 837505 186280 911341 > 4212 [i]