MinT - Best Known (59−42, 59, s)-Nets in Base 8

Best Known (59−42, 59, s)-Nets in Base 8

(59−42, 59, 65)-Net over F₈ — Constructive and digital

Digital (17, 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]

(59−42, 59, 414)-Net in Base 8 — Upper bound on s

There is no (17, 59, 415)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 197899 587118 886102 915821 540308 296156 799729 250322 958154 > 8⁵⁹ [i]