Best Known (128, 128+125, s)-Nets in Base 4
(128, 128+125, 130)-Net over F4 — Constructive and digital
Digital (128, 253, 130)-net over F4, using
- t-expansion [i] based on digital (105, 253, 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
(128, 128+125, 184)-Net over F4 — Digital
Digital (128, 253, 184)-net over F4, using
(128, 128+125, 2182)-Net in Base 4 — Upper bound on s
There is no (128, 253, 2183)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 252, 2183)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 52 899765 525124 872385 929806 723171 778977 443204 822079 956339 327977 446021 323154 537014 776829 811982 085614 870846 179230 036445 620064 103792 329061 488971 810053 799600 > 4252 [i]