MinT - Best Known (81−77, 81, s)-Nets in Base 25

Best Known (81−77, 81, s)-Nets in Base 25

(81−77, 81, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 81, 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]

(81−77, 81, 271)-Net in Base 25 — Upper bound on s

There is no (4, 81, 272)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁸¹, 272, S₂₅, 77), but
- the linear programming bound shows that MÂ â‰¥ 296 675605 806859 748505 162673 034435 115258 648581 017538 394634 857614 710688 110419 391467 911583 863220 751939 183267 298361 101893 533486 872911 453247 070312 500000 / 1705 317125 850348 439457 882817 604799 > 25⁸¹ [i]