MinT - Best Known (37−31, 37, s)-Nets in Base 7

Best Known (37−31, 37, s)-Nets in Base 7

(37−31, 37, 14)-Net over F₇ — Constructive and digital

Digital (6, 37, 14)-net over F₇, using

net from sequence [i] based on digital (6, 13)-sequence over F₇, using
- Niederreiter sequence [i]

(37−31, 37, 24)-Net over F₇ — Digital

Digital (6, 37, 24)-net over F₇, using

t-expansion [i] based on digital (4, 37, 24)-net over F₇, using
- net from sequence [i] based on digital (4, 23)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 4 and N(F) ≥ 24, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(37−31, 37, 92)-Net in Base 7 — Upper bound on s

There is no (6, 37, 93)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7³⁷, 93, S₇, 31), but
- the linear programming bound shows that MÂ â‰¥ 43 118650 177657 635188 235075 948506 944180 769573 300058 389598 719405 573250 / 2 210371 616491 860493 488710 588003 479363 > 7³⁷ [i]