MinT - Best Known (97−75, 97, s)-Nets in Base 5

Best Known (97−75, 97, s)-Nets in Base 5

(97−75, 97, 51)-Net over F₅ — Constructive and digital

Digital (22, 97, 51)-net over F₅, using

net from sequence [i] based on digital (22, 50)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]

(97−75, 97, 119)-Net in Base 5 — Upper bound on s

There is no (22, 97, 120)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁹⁷, 120, S₅, 75), but
- the linear programming bound shows that MÂ â‰¥ 746 789358 749833 717278 577136 021690 038749 008236 536319 760290 325575 624592 602252 960205 078125 / 11 370837 002387 601717 > 5⁹⁷ [i]