MinT - Best Known (15, 15+78, s)-Nets in Base 7

Best Known (15, 15+78, s)-Nets in Base 7

(15, 15+78, 23)-Net over F₇ — Constructive and digital

Digital (15, 93, 23)-net over F₇, using

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

(15, 15+78, 48)-Net over F₇ — Digital

Digital (15, 93, 48)-net over F₇, using

t-expansion [i] based on digital (13, 93, 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+78, 115)-Net in Base 7 — Upper bound on s

There is no (15, 93, 116)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁹³, 116, S₇, 78), but
- the linear programming bound shows that MÂ â‰¥ 1461 050836 965689 717988 085124 237107 129748 746749 166680 135202 043217 134935 457070 725541 224719 632260 787847 / 290 121775 976903 840975 > 7⁹³ [i]