MinT - Best Known (80−76, 80, s)-Nets in Base 25

Best Known (80−76, 80, s)-Nets in Base 25

(80−76, 80, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 80, 66)-net over F₂₅, using

net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
  - a function field by GarcÃa and Quoos [i]

(80−76, 80, 275)-Net in Base 25 — Upper bound on s

There is no (4, 80, 276)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁸⁰, 276, S₂₅, 76), but
- the linear programming bound shows that MÂ â‰¥ 3383 913264 760974 978388 049495 878054 833789 825503 350564 442860 812066 676235 343480 959022 688023 291145 710294 458202 015144 276941 782663 925550 878047 943115 234375 / 488609 824841 595277 415357 808030 039719 > 25⁸⁰ [i]