Best Known (224−100, 224, s)-Nets in Base 4
(224−100, 224, 130)-Net over F4 — Constructive and digital
Digital (124, 224, 130)-net over F4, using
- t-expansion [i] based on digital (105, 224, 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
(224−100, 224, 227)-Net over F4 — Digital
Digital (124, 224, 227)-net over F4, using
(224−100, 224, 3193)-Net in Base 4 — Upper bound on s
There is no (124, 224, 3194)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 735 333403 638695 995307 274147 831022 329225 371433 195704 653426 713935 991315 114677 550595 158888 474771 732359 988689 817975 957252 418429 289716 487308 > 4224 [i]