MinT - Best Known (33, 107, s)-Nets in Base 8

Best Known (33, 107, s)-Nets in Base 8

(33, 107, 65)-Net over F₈ — Constructive and digital

Digital (33, 107, 65)-net over F₈, using

t-expansion [i] based on digital (14, 107, 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]

(33, 107, 97)-Net over F₈ — Digital

Digital (33, 107, 97)-net over F₈, using

t-expansion [i] based on digital (28, 107, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(33, 107, 832)-Net in Base 8 — Upper bound on s

There is no (33, 107, 833)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 297242 721271 984320 288079 966076 198466 356492 156902 255944 078850 020204 800835 165137 235347 114792 973248 > 8¹⁰⁷ [i]