MinT - Best Known (84−80, 84, s)-Nets in Base 25

Best Known (84−80, 84, s)-Nets in Base 25

(84−80, 84, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 84, 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]

(84−80, 84, 264)-Net in Base 25 — Upper bound on s

There is no (4, 84, 265)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁸⁴, 265, S₂₅, 80), but
- the linear programming bound shows that MÂ â‰¥ 48 311239 871958 406516 511931 879610 433824 548490 319414 857381 979413 833662 962555 899974 882002 603654 349011 457257 175960 848527 562774 279431 323520 839214 324951 171875 / 17778 775308 823085 064582 329938 126683 > 25⁸⁴ [i]