Best Known (254−118, 254, s)-Nets in Base 4
(254−118, 254, 130)-Net over F4 — Constructive and digital
Digital (136, 254, 130)-net over F4, using
- t-expansion [i] based on digital (105, 254, 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
(254−118, 254, 224)-Net over F4 — Digital
Digital (136, 254, 224)-net over F4, using
(254−118, 254, 2924)-Net in Base 4 — Upper bound on s
There is no (136, 254, 2925)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 850 695694 511875 574557 725625 296546 224568 013209 434653 370597 372893 879268 217580 025635 784812 185306 617494 803929 328800 166165 920763 713111 390381 398698 310669 916080 > 4254 [i]