Best Known (115, 115+99, s)-Nets in Base 4
(115, 115+99, 130)-Net over F4 — Constructive and digital
Digital (115, 214, 130)-net over F4, using
- t-expansion [i] based on digital (105, 214, 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
(115, 115+99, 195)-Net over F4 — Digital
Digital (115, 214, 195)-net over F4, using
(115, 115+99, 2598)-Net in Base 4 — Upper bound on s
There is no (115, 214, 2599)-net in base 4, because
- 1 times m-reduction [i] would yield (115, 213, 2599)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 176 265639 745404 037807 887207 652126 804421 923375 512129 627500 064472 204490 257824 948172 451985 176298 843067 171411 508518 895941 372943 749312 > 4213 [i]