MinT - Best Known (17, 17+92, s)-Nets in Base 7

Best Known (17, 17+92, s)-Nets in Base 7

(17, 17+92, 25)-Net over F₇ — Constructive and digital

Digital (17, 109, 25)-net over F₇, using

net from sequence [i] based on digital (17, 24)-sequence over F₇, using
- Niederreiter sequence [i]

(17, 17+92, 48)-Net over F₇ — Digital

Digital (17, 109, 48)-net over F₇, using

t-expansion [i] based on digital (13, 109, 48)-net over F₇, using
- net from sequence [i] based on digital (13, 47)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48, using
    - an algebraic function field by Teo [i]

(17, 17+92, 122)-Net in Base 7 — Upper bound on s

There is no (17, 109, 123)-net in base 7, because

2 times m-reduction [i] would yield (17, 107, 123)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7¹⁰⁷, 123, S₇, 90), but
  - the linear programming bound shows that MÂ â‰¥ 27 663775 890020 908036 934524 482207 495821 062948 073408 439000 025068 608013 781461 346879 795902 032422 843230 934357 / 10 064791 997377 > 7¹⁰⁷ [i]