MinT - Best Known (43−32, 43, s)-Nets in Base 5

Best Known (43−32, 43, s)-Nets in Base 5

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

Digital (11, 43, 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]

(43−32, 43, 115)-Net in Base 5 — Upper bound on s

There is no (11, 43, 116)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴³, 116, S₅, 32), but
- the linear programming bound shows that MÂ â‰¥ 78630 206727 363884 575518 018662 709610 896149 980674 684047 698974 609375 000000 000000 / 63839 957809 729412 531818 722179 714129 611818 357811 > 5⁴³ [i]