MinT - Best Known (31−24, 31, s)-Nets in Base 5

Best Known (31−24, 31, s)-Nets in Base 5

(31−24, 31, 22)-Net over F₅ — Constructive and digital

Digital (7, 31, 22)-net over F₅, using

net from sequence [i] based on digital (7, 21)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 7 and N(F) ≥ 22, using
  - an explicitly constructive algebraic function field [i]

(31−24, 31, 75)-Net in Base 5 — Upper bound on s

There is no (7, 31, 76)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5³¹, 76, S₅, 24), but
- the linear programming bound shows that MÂ â‰¥ 10 380941 210094 709978 036051 291913 644167 602062 225341 796875 / 2211 535157 839266 551323 341663 584477 > 5³¹ [i]