Best Known (252−118, 252, s)-Nets in Base 4
(252−118, 252, 130)-Net over F4 — Constructive and digital
Digital (134, 252, 130)-net over F4, using
- t-expansion [i] based on digital (105, 252, 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
(252−118, 252, 217)-Net over F4 — Digital
Digital (134, 252, 217)-net over F4, using
(252−118, 252, 2787)-Net in Base 4 — Upper bound on s
There is no (134, 252, 2788)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 52 597283 985975 376654 692007 112451 109063 981373 590918 594549 545726 734823 731746 596098 784708 725363 674551 639814 288385 775564 750099 154783 235919 543616 283060 971720 > 4252 [i]