Best Known (106, 106+92, s)-Nets in Base 4
(106, 106+92, 130)-Net over F4 — Constructive and digital
Digital (106, 198, 130)-net over F4, using
- t-expansion [i] based on digital (105, 198, 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
(106, 106+92, 179)-Net over F4 — Digital
Digital (106, 198, 179)-net over F4, using
(106, 106+92, 2304)-Net in Base 4 — Upper bound on s
There is no (106, 198, 2305)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 163355 626597 526893 982756 256562 244816 856186 253984 354849 167068 382297 702463 568262 845802 509072 507778 158339 500036 668784 489600 > 4198 [i]