MinT - Best Known (38−32, 38, s)-Nets in Base 7

Best Known (38−32, 38, s)-Nets in Base 7

(38−32, 38, 14)-Net over F₇ — Constructive and digital

Digital (6, 38, 14)-net over F₇, using

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

(38−32, 38, 24)-Net over F₇ — Digital

Digital (6, 38, 24)-net over F₇, using

t-expansion [i] based on digital (4, 38, 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]

(38−32, 38, 89)-Net in Base 7 — Upper bound on s

There is no (6, 38, 90)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7³⁸, 90, S₇, 32), but
- the linear programming bound shows that MÂ â‰¥ 368973 482124 364358 194991 868580 739279 697247 409107 270560 585383 950427 881660 704975 / 2702 047382 108700 165972 616500 269153 651397 200063 > 7³⁸ [i]