MinT - Best Known (65−39, 65, s)-Nets in Base 8

Best Known (65−39, 65, s)-Nets in Base 8

(65−39, 65, 65)-Net over F₈ — Constructive and digital

Digital (26, 65, 65)-net over F₈, using

t-expansion [i] based on digital (14, 65, 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]

(65−39, 65, 86)-Net over F₈ — Digital

Digital (26, 65, 86)-net over F₈, using

t-expansion [i] based on digital (25, 65, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(65−39, 65, 1236)-Net in Base 8 — Upper bound on s

There is no (26, 65, 1237)-net in base 8, because

1 times m-reduction [i] would yield (26, 64, 1237)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6372 948212 678557 286812 618588 248734 982678 144778 534413 609932 > 8⁶⁴ [i]