MinT - Best Known (85−61, 85, s)-Nets in Base 7

Best Known (85−61, 85, s)-Nets in Base 7

(85−61, 85, 30)-Net over F₇ — Constructive and digital

Digital (24, 85, 30)-net over F₇, using

t-expansion [i] based on digital (23, 85, 30)-net over F₇, using
- net from sequence [i] based on digital (23, 29)-sequence over F₇, using
  - Niederreiter sequence [i]

(85−61, 85, 72)-Net over F₇ — Digital

Digital (24, 85, 72)-net over F₇, using

t-expansion [i] based on digital (22, 85, 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]

(85−61, 85, 447)-Net in Base 7 — Upper bound on s

There is no (24, 85, 448)-net in base 7, because

1 times m-reduction [i] would yield (24, 84, 448)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 101665 646046 507327 168307 443104 553188 020652 490254 398128 712100 980861 588609 > 7⁸⁴ [i]