MinT - Best Known (17, 17+82, s)-Nets in Base 7

Best Known (17, 17+82, s)-Nets in Base 7

(17, 17+82, 25)-Net over F₇ — Constructive and digital

Digital (17, 99, 25)-net over F₇, using

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

(17, 17+82, 48)-Net over F₇ — Digital

Digital (17, 99, 48)-net over F₇, using

t-expansion [i] based on digital (13, 99, 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+82, 145)-Net in Base 7 — Upper bound on s

There is no (17, 99, 146)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁹⁹, 146, S₇, 82), but
- the linear programming bound shows that MÂ â‰¥ 39 848707 457928 277108 376826 233038 062785 726777 123598 097048 850564 753795 324206 017740 536263 749677 710224 013769 574267 556126 883990 895834 150811 805802 687498 087209 / 84 370677 026947 316613 807966 680967 163837 485467 503812 377818 646139 002689 > 7⁹⁹ [i]