Best Known (246−122, 246, s)-Nets in Base 4
(246−122, 246, 130)-Net over F4 — Constructive and digital
Digital (124, 246, 130)-net over F4, using
- t-expansion [i] based on digital (105, 246, 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
(246−122, 246, 177)-Net over F4 — Digital
Digital (124, 246, 177)-net over F4, using
(246−122, 246, 2054)-Net in Base 4 — Upper bound on s
There is no (124, 246, 2055)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 13054 170438 603287 714831 395376 117210 653692 166874 780838 346451 132709 293883 244808 892610 883113 610076 100390 272496 633546 958318 498906 720495 508748 840885 938688 > 4246 [i]