MinT - Best Known (54−43, 54, s)-Nets in Base 5

Best Known (54−43, 54, s)-Nets in Base 5

(54−43, 54, 32)-Net over F₅ — Constructive and digital

Digital (11, 54, 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]

(54−43, 54, 67)-Net in Base 5 — Upper bound on s

There is no (11, 54, 68)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵⁴, 68, S₅, 43), but
- the linear programming bound shows that MÂ â‰¥ 144363 514198 442288 716250 914148 986339 569091 796875 / 1917 314091 > 5⁵⁴ [i]