MinT - Best Known (25, 25+34, s)-Nets in Base 7

Best Known (25, 25+34, s)-Nets in Base 7

(25, 25+34, 31)-Net over F₇ — Constructive and digital

Digital (25, 59, 31)-net over F₇, using

net from sequence [i] based on digital (25, 30)-sequence over F₇, using
- Niederreiter sequence [i]

(25, 25+34, 72)-Net over F₇ — Digital

Digital (25, 59, 72)-net over F₇, using

t-expansion [i] based on digital (22, 59, 72)-net over F₇, using
- net from sequence [i] based on digital (22, 71)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 22 and N(F) ≥ 72, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(25, 25+34, 1014)-Net in Base 7 — Upper bound on s

There is no (25, 59, 1015)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 73 373615 358062 116612 938431 100617 829655 807078 873963 > 7⁵⁹ [i]