MinT - Best Known (24, 49, s)-Nets in Base 8

Best Known (24, 49, s)-Nets in Base 8

(24, 49, 69)-Net over F₈ — Constructive and digital

Digital (24, 49, 69)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (3, 15, 24)-net over F₈, using
  - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]
2. digital (9, 34, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(24, 49, 94)-Net over F₈ — Digital

Digital (24, 49, 94)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(24, 49, 3087)-Net in Base 8 — Upper bound on s

There is no (24, 49, 3088)-net in base 8, because

1 times m-reduction [i] would yield (24, 48, 3088)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 22 341847 098630 081073 640041 273138 396504 521159 > 8⁴⁸ [i]