MinT - Best Known (85−81, 85, s)-Nets in Base 25

Best Known (85−81, 85, s)-Nets in Base 25

(85−81, 85, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 85, 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]

(85−81, 85, 263)-Net in Base 25 — Upper bound on s

There is no (4, 85, 264)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁸⁵, 264, S₂₅, 81), but
- the linear programming bound shows that MÂ â‰¥ 45289 578748 730074 256474 042827 425892 047621 998663 239338 156108 911410 518602 833447 715326 764893 840860 701634 002056 029104 643641 858274 349942 803382 873535 156250 000000 / 672222 567253 257920 282468 896151 858599 > 25⁸⁵ [i]