Best Known (125, 125+103, s)-Nets in Base 4
(125, 125+103, 130)-Net over F4 — Constructive and digital
Digital (125, 228, 130)-net over F4, using
- t-expansion [i] based on digital (105, 228, 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
(125, 125+103, 222)-Net over F4 — Digital
Digital (125, 228, 222)-net over F4, using
(125, 125+103, 3124)-Net in Base 4 — Upper bound on s
There is no (125, 228, 3125)-net in base 4, because
- 1 times m-reduction [i] would yield (125, 227, 3125)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 47218 267038 863801 262108 014336 291317 650455 917354 151807 914055 622074 235253 350660 643957 597002 722650 131824 372693 218569 276069 611059 232393 227876 > 4227 [i]