MinT - Best Known (53−42, 53, s)-Nets in Base 5

Best Known (53−42, 53, s)-Nets in Base 5

(53−42, 53, 32)-Net over F₅ — Constructive and digital

Digital (11, 53, 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]

(53−42, 53, 68)-Net in Base 5 — Upper bound on s

There is no (11, 53, 69)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵³, 69, S₅, 42), but
- the linear programming bound shows that MÂ â‰¥ 32 481587 176891 313362 148139 276541 769504 547119 140625 / 2 799758 136448 > 5⁵³ [i]