MinT - Best Known (109−93, 109, s)-Nets in Base 7

Best Known (109−93, 109, s)-Nets in Base 7

(109−93, 109, 24)-Net over F₇ — Constructive and digital

Digital (16, 109, 24)-net over F₇, using

net from sequence [i] based on digital (16, 23)-sequence over F₇, using
- Niederreiter sequence [i]

(109−93, 109, 48)-Net over F₇ — Digital

Digital (16, 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]

(109−93, 109, 115)-Net in Base 7 — Upper bound on s

There is no (16, 109, 116)-net in base 7, because

4 times m-reduction [i] would yield (16, 105, 116)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7¹⁰⁵, 116, S₇, 89), but
  - the linear programming bound shows that MÂ â‰¥ 83 666546 653535 939552 480855 743847 612950 700869 329982 478928 196991 304032 769691 674719 729308 153962 596677 / 1472 063949 > 7¹⁰⁵ [i]