Best Known (125, 125+118, s)-Nets in Base 4
(125, 125+118, 130)-Net over F4 — Constructive and digital
Digital (125, 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
(125, 125+118, 187)-Net over F4 — Digital
Digital (125, 243, 187)-net over F4, using
(125, 125+118, 2247)-Net in Base 4 — Upper bound on s
There is no (125, 243, 2248)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 203 498322 956786 843514 311889 052943 283892 611326 126828 109669 938034 852105 918362 435944 138105 610902 386420 496415 569666 993493 826238 570996 480495 635611 101816 > 4243 [i]