Best Known (135, 135+108, s)-Nets in Base 4
(135, 135+108, 130)-Net over F4 — Constructive and digital
Digital (135, 243, 130)-net over F4, using
- t-expansion [i] based on digital (105, 243, 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+108, 247)-Net over F4 — Digital
Digital (135, 243, 247)-net over F4, using
(135, 135+108, 3534)-Net in Base 4 — Upper bound on s
There is no (135, 243, 3535)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 202 423201 751558 009382 879626 988526 260603 344009 272806 297154 191781 618995 417165 683246 892721 108306 872145 303798 133902 577229 666163 131384 793552 634952 422260 > 4243 [i]