MinT - Best Known (71−47, 71, s)-Nets in Base 7

Best Known (71−47, 71, s)-Nets in Base 7

(71−47, 71, 30)-Net over F₇ — Constructive and digital

Digital (24, 71, 30)-net over F₇, using

t-expansion [i] based on digital (23, 71, 30)-net over F₇, using
- net from sequence [i] based on digital (23, 29)-sequence over F₇, using
  - Niederreiter sequence [i]

(71−47, 71, 72)-Net over F₇ — Digital

Digital (24, 71, 72)-net over F₇, using

t-expansion [i] based on digital (22, 71, 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]

(71−47, 71, 571)-Net in Base 7 — Upper bound on s

There is no (24, 71, 572)-net in base 7, because

1 times m-reduction [i] would yield (24, 70, 572)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 144138 729333 499546 846069 562516 305558 327708 855445 020626 059425 > 7⁷⁰ [i]