MinT - Best Known (43−34, 43, s)-Nets in Base 5

Best Known (43−34, 43, s)-Nets in Base 5

(43−34, 43, 26)-Net over F₅ — Constructive and digital

Digital (9, 43, 26)-net over F₅, using

net from sequence [i] based on digital (9, 25)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
  - an explicitly constructive algebraic function field [i]

(43−34, 43, 68)-Net in Base 5 — Upper bound on s

There is no (9, 43, 69)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴³, 69, S₅, 34), but
- the linear programming bound shows that MÂ â‰¥ 4679 364838 452356 280384 947240 236215 293407 440185 546875 / 3979 587995 901421 617168 > 5⁴³ [i]