Best Known (124, 124+126, s)-Nets in Base 4
(124, 124+126, 130)-Net over F4 — Constructive and digital
Digital (124, 250, 130)-net over F4, using
- t-expansion [i] based on digital (105, 250, 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
(124, 124+126, 171)-Net over F4 — Digital
Digital (124, 250, 171)-net over F4, using
(124, 124+126, 1933)-Net in Base 4 — Upper bound on s
There is no (124, 250, 1934)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 365300 592214 105529 157342 887512 596932 283987 984185 071535 391347 486117 557862 654630 646348 028886 826843 385331 217926 956058 448089 446005 274737 222112 096708 914880 > 4250 [i]