MinT - Best Known (25, 25+41, s)-Nets in Base 7

Best Known (25, 25+41, s)-Nets in Base 7

(25, 25+41, 31)-Net over F₇ — Constructive and digital

Digital (25, 66, 31)-net over F₇, using

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

(25, 25+41, 72)-Net over F₇ — Digital

Digital (25, 66, 72)-net over F₇, using

t-expansion [i] based on digital (22, 66, 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+41, 759)-Net in Base 7 — Upper bound on s

There is no (25, 66, 760)-net in base 7, because

1 times m-reduction [i] would yield (25, 65, 760)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 8 666497 997865 919826 435253 455128 669277 758151 013798 315073 > 7⁶⁵ [i]