MinT - Best Known (25, 25+65, s)-Nets in Base 7

Best Known (25, 25+65, s)-Nets in Base 7

(25, 25+65, 31)-Net over F₇ — Constructive and digital

Digital (25, 90, 31)-net over F₇, using

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

(25, 25+65, 72)-Net over F₇ — Digital

Digital (25, 90, 72)-net over F₇, using

t-expansion [i] based on digital (22, 90, 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+65, 457)-Net in Base 7 — Upper bound on s

There is no (25, 90, 458)-net in base 7, because

1 times m-reduction [i] would yield (25, 89, 458)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1730 965020 294916 722287 260744 760870 580519 014271 506228 365382 596964 766891 814465 > 7⁸⁹ [i]