Best Known (248−125, 248, s)-Nets in Base 4
(248−125, 248, 130)-Net over F4 — Constructive and digital
Digital (123, 248, 130)-net over F4, using
- t-expansion [i] based on digital (105, 248, 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
(248−125, 248, 170)-Net over F4 — Digital
Digital (123, 248, 170)-net over F4, using
(248−125, 248, 1946)-Net in Base 4 — Upper bound on s
There is no (123, 248, 1947)-net in base 4, because
- 1 times m-reduction [i] would yield (123, 247, 1947)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 52015 106510 369675 200116 019647 580290 542225 640285 582362 869438 206016 133126 753835 319582 102280 981596 968318 366726 770551 029779 210753 328987 568913 896130 109280 > 4247 [i]