MinT - Best Known (32, 32+71, s)-Nets in Base 8

Best Known (32, 32+71, s)-Nets in Base 8

(32, 32+71, 65)-Net over F₈ — Constructive and digital

Digital (32, 103, 65)-net over F₈, using

t-expansion [i] based on digital (14, 103, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(32, 32+71, 97)-Net over F₈ — Digital

Digital (32, 103, 97)-net over F₈, using

t-expansion [i] based on digital (28, 103, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(32, 32+71, 829)-Net in Base 8 — Upper bound on s

There is no (32, 103, 830)-net in base 8, because

1 times m-reduction [i] would yield (32, 102, 830)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 133 818011 191270 082893 044336 797610 035963 080902 875832 906892 892615 227186 608723 701484 446893 709566 > 8¹⁰² [i]