MinT - Best Known (109−103, 109, s)-Nets in Base 7

Best Known (109−103, 109, s)-Nets in Base 7

(109−103, 109, 14)-Net over F₇ — Constructive and digital

Digital (6, 109, 14)-net over F₇, using

net from sequence [i] based on digital (6, 13)-sequence over F₇, using
- Niederreiter sequence [i]

(109−103, 109, 24)-Net over F₇ — Digital

Digital (6, 109, 24)-net over F₇, using

t-expansion [i] based on digital (4, 109, 24)-net over F₇, using
- net from sequence [i] based on digital (4, 23)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 4 and N(F) ≥ 24, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(109−103, 109, 50)-Net in Base 7 — Upper bound on s

There is no (6, 109, 51)-net in base 7, because

10 times m-reduction [i] would yield (6, 99, 51)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7⁹⁹, 51, S₇, 2, 93), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 25 875812 076998 063930 757182 152801 734486 857625 591237 003207 471162 651133 531677 095424 480008 / 47 > 7⁹⁹ [i]