MinT - Best Known (6, 40, s)-Nets in Base 7

Best Known (6, 40, s)-Nets in Base 7

(6, 40, 14)-Net over F₇ — Constructive and digital

Digital (6, 40, 14)-net over F₇, using

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

(6, 40, 24)-Net over F₇ — Digital

Digital (6, 40, 24)-net over F₇, using

t-expansion [i] based on digital (4, 40, 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]

(6, 40, 81)-Net in Base 7 — Upper bound on s

There is no (6, 40, 82)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁴⁰, 82, S₇, 34), but
- the linear programming bound shows that MÂ â‰¥ 673801 835639 757875 439893 433054 141969 823267 481754 608782 979429 709503 946935 / 95 010891 095162 431216 453370 367168 062378 > 7⁴⁰ [i]