MinT - Best Known (58−41, 58, s)-Nets in Base 5

Best Known (58−41, 58, s)-Nets in Base 5

(58−41, 58, 42)-Net over F₅ — Constructive and digital

Digital (17, 58, 42)-net over F₅, using

net from sequence [i] based on digital (17, 41)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 17 and N(F) ≥ 42, using
  - an explicitly constructive algebraic function field [i]

(58−41, 58, 186)-Net in Base 5 — Upper bound on s

There is no (17, 58, 187)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵⁸, 187, S₅, 41), but
- the linear programming bound shows that MÂ â‰¥ 1421 745148 431060 228032 080609 413368 612436 550082 141711 052104 972337 914290 392291 150055 825710 296630 859375 / 38972 212876 244344 831445 410530 619908 364598 002815 349240 750459 > 5⁵⁸ [i]