MinT - Best Known (44−35, 44, s)-Nets in Base 5

Best Known (44−35, 44, s)-Nets in Base 5

(44−35, 44, 26)-Net over F₅ — Constructive and digital

Digital (9, 44, 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]

(44−35, 44, 63)-Net in Base 5 — Upper bound on s

There is no (9, 44, 64)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴⁴, 64, S₅, 35), but
- the linear programming bound shows that MÂ â‰¥ 9336 202228 364953 725758 823566 138744 354248 046875 / 1625 725890 251463 > 5⁴⁴ [i]