Best Known (247−120, 247, s)-Nets in Base 4
(247−120, 247, 130)-Net over F4 — Constructive and digital
Digital (127, 247, 130)-net over F4, using
- t-expansion [i] based on digital (105, 247, 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
(247−120, 247, 190)-Net over F4 — Digital
Digital (127, 247, 190)-net over F4, using
(247−120, 247, 2277)-Net in Base 4 — Upper bound on s
There is no (127, 247, 2278)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 52002 800403 788125 732398 742497 137803 121910 835939 292932 357966 186326 065063 104005 052444 116978 106259 716506 477619 007939 973406 028442 095455 759472 025629 815720 > 4247 [i]