MinT - Best Known (136−103, 136, s)-Nets in Base 8

Best Known (136−103, 136, s)-Nets in Base 8

(136−103, 136, 65)-Net over F₈ — Constructive and digital

Digital (33, 136, 65)-net over F₈, using

t-expansion [i] based on digital (14, 136, 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]

(136−103, 136, 97)-Net over F₈ — Digital

Digital (33, 136, 97)-net over F₈, using

t-expansion [i] based on digital (28, 136, 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]

(136−103, 136, 665)-Net in Base 8 — Upper bound on s

There is no (33, 136, 666)-net in base 8, because

1 times m-reduction [i] would yield (33, 135, 666)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 87 282892 219187 842303 261604 130144 441114 262700 444628 766918 510039 769333 550187 943018 890887 618959 583750 688782 119637 694575 783568 > 8¹³⁵ [i]