Best Known (235−115, 235, s)-Nets in Base 4
(235−115, 235, 130)-Net over F4 — Constructive and digital
Digital (120, 235, 130)-net over F4, using
- t-expansion [i] based on digital (105, 235, 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
(235−115, 235, 177)-Net over F4 — Digital
Digital (120, 235, 177)-net over F4, using
(235−115, 235, 2133)-Net in Base 4 — Upper bound on s
There is no (120, 235, 2134)-net in base 4, because
- 1 times m-reduction [i] would yield (120, 234, 2134)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 771 249049 549320 125723 879505 537563 556322 122528 441237 478092 035904 380328 094833 940836 633418 774485 915071 285438 288236 105748 979177 455922 153970 223560 > 4234 [i]