Best Known (135, 135+118, s)-Nets in Base 4
(135, 135+118, 130)-Net over F4 — Constructive and digital
Digital (135, 253, 130)-net over F4, using
- t-expansion [i] based on digital (105, 253, 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
(135, 135+118, 221)-Net over F4 — Digital
Digital (135, 253, 221)-net over F4, using
(135, 135+118, 2855)-Net in Base 4 — Upper bound on s
There is no (135, 253, 2856)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 212 856393 136765 613938 055752 077133 050991 972613 172593 714305 323593 447597 225141 176597 040808 124238 481240 890827 293361 115084 261956 262454 303816 494504 250662 895712 > 4253 [i]