MinT - Best Known (109−95, 109, s)-Nets in Base 7

Best Known (109−95, 109, s)-Nets in Base 7

(109−95, 109, 22)-Net over F₇ — Constructive and digital

Digital (14, 109, 22)-net over F₇, using

net from sequence [i] based on digital (14, 21)-sequence over F₇, using
- Niederreiter sequence [i]

(109−95, 109, 48)-Net over F₇ — Digital

Digital (14, 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]

(109−95, 109, 103)-Net in Base 7 — Upper bound on s

There is no (14, 109, 104)-net in base 7, because

16 times m-reduction [i] would yield (14, 93, 104)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7⁹³, 104, S₇, 79), but
  - the linear programming bound shows that MÂ â‰¥ 102 796001 257782 760535 416925 163152 954679 750355 892884 319229 097355 706999 500295 924643 679507 / 22 256456 > 7⁹³ [i]