MinT - Best Known (116−81, 116, s)-Nets in Base 8

Best Known (116−81, 116, s)-Nets in Base 8

(116−81, 116, 65)-Net over F₈ — Constructive and digital

Digital (35, 116, 65)-net over F₈, using

t-expansion [i] based on digital (14, 116, 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]

(116−81, 116, 112)-Net over F₈ — Digital

Digital (35, 116, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(116−81, 116, 864)-Net in Base 8 — Upper bound on s

There is no (35, 116, 865)-net in base 8, because

1 times m-reduction [i] would yield (35, 115, 865)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 73 765824 081141 378639 366150 637763 247442 573574 156094 793479 874913 545896 901724 331613 702177 847803 292376 032456 > 8¹¹⁵ [i]