MinT - Best Known (63−40, 63, s)-Nets in Base 7

Best Known (63−40, 63, s)-Nets in Base 7

(63−40, 63, 30)-Net over F₇ — Constructive and digital

Digital (23, 63, 30)-net over F₇, using

net from sequence [i] based on digital (23, 29)-sequence over F₇, using
- Niederreiter sequence [i]

(63−40, 63, 72)-Net over F₇ — Digital

Digital (23, 63, 72)-net over F₇, using

t-expansion [i] based on digital (22, 63, 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]

(63−40, 63, 622)-Net in Base 7 — Upper bound on s

There is no (23, 63, 623)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 174833 600538 860011 964610 963616 187936 055695 271046 974601 > 7⁶³ [i]