MinT - Best Known (59−37, 59, s)-Nets in Base 8

Best Known (59−37, 59, s)-Nets in Base 8

(59−37, 59, 65)-Net over F₈ — Constructive and digital

Digital (22, 59, 65)-net over F₈, using

t-expansion [i] based on digital (14, 59, 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]

(59−37, 59, 76)-Net over F₈ — Digital

Digital (22, 59, 76)-net over F₈, using

t-expansion [i] based on digital (20, 59, 76)-net over F₈, using
- net from sequence [i] based on digital (20, 75)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 20 and N(F) ≥ 76, using
    - a curve from the manYPoints database [i]

(59−37, 59, 865)-Net in Base 8 — Upper bound on s

There is no (22, 59, 866)-net in base 8, because

1 times m-reduction [i] would yield (22, 58, 866)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23969 797656 102227 329277 094437 420682 201462 327993 250480 > 8⁵⁸ [i]