Best Known (243−110, 243, s)-Nets in Base 4
(243−110, 243, 130)-Net over F4 — Constructive and digital
Digital (133, 243, 130)-net over F4, using
- t-expansion [i] based on digital (105, 243, 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
(243−110, 243, 234)-Net over F4 — Digital
Digital (133, 243, 234)-net over F4, using
(243−110, 243, 3206)-Net in Base 4 — Upper bound on s
There is no (133, 243, 3207)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 202 746917 970584 224845 861964 535473 983116 555517 887228 313799 100251 430167 226867 484547 077269 963403 624340 786401 265069 980272 616333 752493 762680 584081 711840 > 4243 [i]