MinT - Best Known (78−74, 78, s)-Nets in Base 25

Best Known (78−74, 78, s)-Nets in Base 25

(78−74, 78, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 78, 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]

(78−74, 78, 283)-Net in Base 25 — Upper bound on s

There is no (4, 78, 284)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁷⁸, 284, S₂₅, 74), but
- the linear programming bound shows that MÂ â‰¥ 37 008286 106645 307943 583756 755056 575871 344199 160394 895930 475860 077342 479924 847599 480086 252713 461634 353199 654345 889513 251677 271910 011768 341064 453125 / 3 375799 960178 170273 295895 906613 108093 > 25⁷⁸ [i]