MinT - Best Known (15, 116, s)-Nets in Base 9

Best Known (15, 116, s)-Nets in Base 9

(15, 116, 64)-Net over F₉ — Constructive and digital

Digital (15, 116, 64)-net over F₉, using

t-expansion [i] based on digital (13, 116, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(15, 116, 142)-Net in Base 9 — Upper bound on s

There is no (15, 116, 143)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9¹¹⁶, 143, S₉, 101), but
- the linear programming bound shows that MÂ â‰¥ 109659 729681 379295 512842 223941 662357 119688 792859 974740 569500 657494 850073 924570 405565 163826 885778 712563 102002 992093 255200 204578 992165 878041 / 206 699921 658510 089797 064000 > 9¹¹⁶ [i]