MinT - Best Known (83−79, 83, s)-Nets in Base 25

Best Known (83−79, 83, s)-Nets in Base 25

(83−79, 83, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 83, 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]

(83−79, 83, 265)-Net in Base 25 — Upper bound on s

There is no (4, 83, 266)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁸³, 266, S₂₅, 79), but
- the linear programming bound shows that MÂ â‰¥ 8764 881963 493724 880020 800622 067046 352874 826016 473092 560034 805981 779274 123703 703139 695023 078109 522189 974283 506996 854953 285946 976393 461227 416992 187500 / 81 321931 725186 289794 219718 845063 > 25⁸³ [i]