MinT - Best Known (51−40, 51, s)-Nets in Base 5

Best Known (51−40, 51, s)-Nets in Base 5

(51−40, 51, 32)-Net over F₅ — Constructive and digital

Digital (11, 51, 32)-net over F₅, using

net from sequence [i] based on digital (11, 31)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 11 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]

(51−40, 51, 78)-Net in Base 5 — Upper bound on s

There is no (11, 51, 79)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵¹, 79, S₅, 40), but
- the linear programming bound shows that MÂ â‰¥ 14867 213313 125097 735312 163393 928130 972199 141979 217529 296875 / 32679 485863 439789 157723 > 5⁵¹ [i]