Best Known (128, 128+104, s)-Nets in Base 4
(128, 128+104, 130)-Net over F4 — Constructive and digital
Digital (128, 232, 130)-net over F4, using
- t-expansion [i] based on digital (105, 232, 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
(128, 128+104, 231)-Net over F4 — Digital
Digital (128, 232, 231)-net over F4, using
(128, 128+104, 3229)-Net in Base 4 — Upper bound on s
There is no (128, 232, 3230)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 47 668274 036918 459062 374195 482721 231577 168018 191532 358342 375212 436683 352330 807116 387246 724910 728929 575443 394990 384839 907043 935262 653249 340516 > 4232 [i]