Best Known (247−110, 247, s)-Nets in Base 4
(247−110, 247, 130)-Net over F4 — Constructive and digital
Digital (137, 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
(247−110, 247, 249)-Net over F4 — Digital
Digital (137, 247, 249)-net over F4, using
(247−110, 247, 3550)-Net in Base 4 — Upper bound on s
There is no (137, 247, 3551)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 51149 692853 311999 375695 855285 997591 708137 363437 618921 419877 481000 046732 329276 533958 602818 962220 158146 594513 922340 383384 231742 115252 172525 057768 148792 > 4247 [i]