Best Known (252−126, 252, s)-Nets in Base 4
(252−126, 252, 130)-Net over F4 — Constructive and digital
Digital (126, 252, 130)-net over F4, using
- t-expansion [i] based on digital (105, 252, 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
(252−126, 252, 177)-Net over F4 — Digital
Digital (126, 252, 177)-net over F4, using
(252−126, 252, 2022)-Net in Base 4 — Upper bound on s
There is no (126, 252, 2023)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 53 341072 093706 197607 589057 040079 553383 665182 143993 979952 389666 793891 668292 573381 509269 921498 501346 072721 967360 983978 773598 731930 094302 051176 939161 472800 > 4252 [i]