Best Known (249−122, 249, s)-Nets in Base 4
(249−122, 249, 130)-Net over F4 — Constructive and digital
Digital (127, 249, 130)-net over F4, using
- t-expansion [i] based on digital (105, 249, 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
(249−122, 249, 186)-Net over F4 — Digital
Digital (127, 249, 186)-net over F4, using
(249−122, 249, 2202)-Net in Base 4 — Upper bound on s
There is no (127, 249, 2203)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 824613 625704 100927 533832 710700 381526 770368 835784 146200 880685 166329 109686 411515 712361 763665 340713 382656 533378 841023 539098 367960 336185 655190 417237 310400 > 4249 [i]