MinT - Best Known (41−22, 41, s)-Nets in Base 8

Best Known (41−22, 41, s)-Nets in Base 8

(41−22, 41, 65)-Net over F₈ — Constructive and digital

Digital (19, 41, 65)-net over F₈, using

t-expansion [i] based on digital (14, 41, 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]

(41−22, 41, 69)-Net over F₈ — Digital

Digital (19, 41, 69)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(41−22, 41, 1622)-Net in Base 8 — Upper bound on s

There is no (19, 41, 1623)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 658719 362927 550699 960021 442790 119192 > 8⁴¹ [i]