MinT - Best Known (7, 7+27, s)-Nets in Base 5

Best Known (7, 7+27, s)-Nets in Base 5

(7, 7+27, 22)-Net over F₅ — Constructive and digital

Digital (7, 34, 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]

(7, 7+27, 64)-Net in Base 5 — Upper bound on s

There is no (7, 34, 65)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5³⁴, 65, S₅, 27), but
- the linear programming bound shows that MÂ â‰¥ 64 241548 253700 687835 401117 197195 381929 859807 132743 299007 415771 484375 / 105 626721 073484 056311 392841 841080 747283 817551 > 5³⁴ [i]