Best Known (136, 136+115, s)-Nets in Base 4
(136, 136+115, 130)-Net over F4 — Constructive and digital
Digital (136, 251, 130)-net over F4, using
- t-expansion [i] based on digital (105, 251, 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
(136, 136+115, 232)-Net over F4 — Digital
Digital (136, 251, 232)-net over F4, using
(136, 136+115, 3170)-Net in Base 4 — Upper bound on s
There is no (136, 251, 3171)-net in base 4, because
- 1 times m-reduction [i] would yield (136, 250, 3171)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3 300415 811007 079500 151342 126990 106254 889637 923673 278784 435692 365105 881182 961977 676971 152347 423162 828560 829260 752762 569492 870588 726072 223873 619308 909840 > 4250 [i]