MinT - Best Known (25, 25+67, s)-Nets in Base 7

Best Known (25, 25+67, s)-Nets in Base 7

(25, 25+67, 31)-Net over F₇ — Constructive and digital

Digital (25, 92, 31)-net over F₇, using

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

(25, 25+67, 72)-Net over F₇ — Digital

Digital (25, 92, 72)-net over F₇, using

t-expansion [i] based on digital (22, 92, 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+67, 448)-Net in Base 7 — Upper bound on s

There is no (25, 92, 449)-net in base 7, because

1 times m-reduction [i] would yield (25, 91, 449)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 84211 139006 308737 891524 058900 950932 990135 293123 425374 161542 746429 344193 845127 > 7⁹¹ [i]