Best Known (115, 115+101, s)-Nets in Base 4
(115, 115+101, 130)-Net over F4 — Constructive and digital
Digital (115, 216, 130)-net over F4, using
- t-expansion [i] based on digital (105, 216, 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+101, 190)-Net over F4 — Digital
Digital (115, 216, 190)-net over F4, using
(115, 115+101, 2479)-Net in Base 4 — Upper bound on s
There is no (115, 216, 2480)-net in base 4, because
- 1 times m-reduction [i] would yield (115, 215, 2480)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2824 028298 300041 962070 066511 975908 538579 690759 679938 472862 348608 904884 904823 266019 228951 453095 942328 664227 520361 891864 929070 978536 > 4215 [i]