MinT - Best Known (135−105, 135, s)-Nets in Base 8

Best Known (135−105, 135, s)-Nets in Base 8

(135−105, 135, 65)-Net over F₈ — Constructive and digital

Digital (30, 135, 65)-net over F₈, using

t-expansion [i] based on digital (14, 135, 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]

(135−105, 135, 97)-Net over F₈ — Digital

Digital (30, 135, 97)-net over F₈, using

t-expansion [i] based on digital (28, 135, 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]

(135−105, 135, 581)-Net in Base 8 — Upper bound on s

There is no (30, 135, 582)-net in base 8, because

1 times m-reduction [i] would yield (30, 134, 582)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 916483 977051 205496 386365 871145 248911 411142 338828 801816 866113 587660 287250 738384 806546 446080 999630 899514 739361 313320 081212 > 8¹³⁴ [i]