MinT - Best Known (39−33, 39, s)-Nets in Base 7

Best Known (39−33, 39, s)-Nets in Base 7

(39−33, 39, 14)-Net over F₇ — Constructive and digital

Digital (6, 39, 14)-net over F₇, using

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

(39−33, 39, 24)-Net over F₇ — Digital

Digital (6, 39, 24)-net over F₇, using

t-expansion [i] based on digital (4, 39, 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]

(39−33, 39, 85)-Net in Base 7 — Upper bound on s

There is no (6, 39, 86)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7³⁹, 86, S₇, 33), but
- the linear programming bound shows that MÂ â‰¥ 527 008080 494279 856170 892078 232357 193037 384429 361572 005984 560352 539930 535495 / 575217 199177 512121 852479 161597 335674 570167 > 7³⁹ [i]