MinT - Best Known (11, 11+∞, s)-Nets in Base 7

Best Known (11, 11+∞, s)-Nets in Base 7

(11, 11+∞, 19)-Net over F₇ — Constructive and digital

Digital (11, m, 19)-net over F₇ for arbitrarily large m, using

net from sequence [i] based on digital (11, 18)-sequence over F₇, using
- Niederreiter sequence [i]

(11, 11+∞, 38)-Net over F₇ — Digital

Digital (11, m, 38)-net over F₇ for arbitrarily large m, using

net from sequence [i] based on digital (11, 37)-sequence over F₇, using
- t-expansion [i] based on digital (9, 37)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 9 and N(F) ≥ 38, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(11, 11+∞, 82)-Net in Base 7 — Upper bound on s

There is no (11, m, 83)-net in base 7 for arbitrarily large m, because

m-reduction [i] would yield (11, 163, 83)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7¹⁶³, 83, S₇, 2, 152), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 11 835859 933879 651892 576153 957238 792240 080254 933375 367749 393514 926892 794094 745159 685194 095824 462886 799654 218773 301668 178947 835203 321689 895203 / 17 > 7¹⁶³ [i]