MinT - Best Known (31, 31+72, s)-Nets in Base 8

Best Known (31, 31+72, s)-Nets in Base 8

(31, 31+72, 65)-Net over F₈ — Constructive and digital

Digital (31, 103, 65)-net over F₈, using

t-expansion [i] based on digital (14, 103, 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]

(31, 31+72, 97)-Net over F₈ — Digital

Digital (31, 103, 97)-net over F₈, using

t-expansion [i] based on digital (28, 103, 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]

(31, 31+72, 760)-Net in Base 8 — Upper bound on s

There is no (31, 103, 761)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1089 688320 558199 038842 456190 982872 318009 967097 863216 278171 461471 212961 038259 064993 920236 533858 > 8¹⁰³ [i]