Best Known (118, 118+78, s)-Nets in Base 4
(118, 118+78, 130)-Net over F4 — Constructive and digital
Digital (118, 196, 130)-net over F4, using
- t-expansion [i] based on digital (105, 196, 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
(118, 118+78, 292)-Net over F4 — Digital
Digital (118, 196, 292)-net over F4, using
(118, 118+78, 5413)-Net in Base 4 — Upper bound on s
There is no (118, 196, 5414)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 10114 587121 680859 429267 719865 798183 033989 390353 622220 741744 704056 716268 333315 437112 787432 678055 266750 349665 087254 010544 > 4196 [i]