MinT - Best Known (6, ∞, s)-Nets in Base 7

Best Known (6, ∞, s)-Nets in Base 7

(6, ∞, 14)-Net over F₇ — Constructive and digital

Digital (6, m, 14)-net over F₇ for arbitrarily large m, using

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

(6, ∞, 24)-Net over F₇ — Digital

Digital (6, m, 24)-net over F₇ for arbitrarily large m, using

net from sequence [i] based on digital (6, 23)-sequence over F₇, using
- t-expansion [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]

(6, ∞, 50)-Net in Base 7 — Upper bound on s

There is no (6, m, 51)-net in base 7 for arbitrarily large m, because

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]