MinT - Best Known (32, 32+119, s)-Nets in Base 8

Best Known (32, 32+119, s)-Nets in Base 8

(32, 32+119, 65)-Net over F₈ — Constructive and digital

Digital (32, 151, 65)-net over F₈, using

t-expansion [i] based on digital (14, 151, 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+119, 97)-Net over F₈ — Digital

Digital (32, 151, 97)-net over F₈, using

t-expansion [i] based on digital (28, 151, 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+119, 607)-Net in Base 8 — Upper bound on s

There is no (32, 151, 608)-net in base 8, because

1 times m-reduction [i] would yield (32, 150, 608)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2980 459405 742662 841403 552453 480435 570100 907965 770287 063248 576838 083918 083546 138772 992897 458780 382346 181498 219340 660275 654385 558906 145590 > 8¹⁵⁰ [i]