MinT - Best Known (31, 31+123, s)-Nets in Base 8

Best Known (31, 31+123, s)-Nets in Base 8

(31, 31+123, 65)-Net over F₈ — Constructive and digital

Digital (31, 154, 65)-net over F₈, using

t-expansion [i] based on digital (14, 154, 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+123, 97)-Net over F₈ — Digital

Digital (31, 154, 97)-net over F₈, using

t-expansion [i] based on digital (28, 154, 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+123, 581)-Net in Base 8 — Upper bound on s

There is no (31, 154, 582)-net in base 8, because

1 times m-reduction [i] would yield (31, 153, 582)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 518488 904621 649130 456265 507938 285637 988752 880116 488480 366848 599552 637463 000681 261142 171855 043147 865728 445519 787906 184533 029204 471627 022680 > 8¹⁵³ [i]