Best Known (113, 113+86, s)-Nets in Base 4
(113, 113+86, 130)-Net over F4 — Constructive and digital
Digital (113, 199, 130)-net over F4, using
- t-expansion [i] based on digital (105, 199, 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
(113, 113+86, 227)-Net over F4 — Digital
Digital (113, 199, 227)-net over F4, using
(113, 113+86, 3405)-Net in Base 4 — Upper bound on s
There is no (113, 199, 3406)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 650979 000766 418799 868894 137436 111493 978762 163642 471735 182862 288202 033661 289011 660899 792059 952522 577786 478382 991153 652844 > 4199 [i]