MinT - Best Known (93−71, 93, s)-Nets in Base 5

Best Known (93−71, 93, s)-Nets in Base 5

(93−71, 93, 51)-Net over F₅ — Constructive and digital

Digital (22, 93, 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]

(93−71, 93, 131)-Net in Base 5 — Upper bound on s

There is no (22, 93, 132)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁹³, 132, S₅, 71), but
- the linear programming bound shows that MÂ â‰¥ 25549 291733 415442 151234 980320 043197 136920 092288 343553 022792 996602 848003 551144 984157 872386 276721 954345 703125 / 241246 731132 013925 778289 319682 864890 093568 > 5⁹³ [i]