MinT - Best Known (38−29, 38, s)-Nets in Base 5

Best Known (38−29, 38, s)-Nets in Base 5

(38−29, 38, 26)-Net over F₅ — Constructive and digital

Digital (9, 38, 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]

(38−29, 38, 92)-Net in Base 5 — Upper bound on s

There is no (9, 38, 93)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5³⁸, 93, S₅, 29), but
- the linear programming bound shows that MÂ â‰¥ 2002 621299 788624 721545 787649 809762 379060 153770 446777 343750 000000 000000 / 5 101057 776596 581936 933578 939671 966304 165353 > 5³⁸ [i]