MinT - Best Known (15, 15+82, s)-Nets in Base 7

Best Known (15, 15+82, s)-Nets in Base 7

(15, 15+82, 23)-Net over F₇ — Constructive and digital

Digital (15, 97, 23)-net over F₇, using

net from sequence [i] based on digital (15, 22)-sequence over F₇, using
- Niederreiter sequence [i]

(15, 15+82, 48)-Net over F₇ — Digital

Digital (15, 97, 48)-net over F₇, using

t-expansion [i] based on digital (13, 97, 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]

(15, 15+82, 110)-Net in Base 7 — Upper bound on s

There is no (15, 97, 111)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁹⁷, 111, S₇, 82), but
- the linear programming bound shows that MÂ â‰¥ 62788 976904 680796 248175 127161 381680 344067 474062 884583 229696 137180 937528 884756 703433 435942 187763 / 5 520522 093125 > 7⁹⁷ [i]