Best Known (115, 115+104, s)-Nets in Base 4
(115, 115+104, 130)-Net over F4 — Constructive and digital
Digital (115, 219, 130)-net over F4, using
- t-expansion [i] based on digital (105, 219, 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+104, 183)-Net over F4 — Digital
Digital (115, 219, 183)-net over F4, using
(115, 115+104, 2271)-Net in Base 4 — Upper bound on s
There is no (115, 219, 2272)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 717386 145353 167454 020726 400309 928974 342072 451533 874064 646581 870844 741292 910948 289870 344142 880295 956656 939319 334435 951205 970597 020410 > 4219 [i]