MinT - Best Known (31, 31+142, s)-Nets in Base 8

Best Known (31, 31+142, s)-Nets in Base 8

(31, 31+142, 65)-Net over F₈ — Constructive and digital

Digital (31, 173, 65)-net over F₈, using

t-expansion [i] based on digital (14, 173, 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+142, 97)-Net over F₈ — Digital

Digital (31, 173, 97)-net over F₈, using

t-expansion [i] based on digital (28, 173, 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+142, 573)-Net in Base 8 — Upper bound on s

There is no (31, 173, 574)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 742907 888749 843214 857673 030173 458525 903799 313673 664688 256043 305769 167016 941619 982937 298784 595846 610211 283808 956414 900189 609894 033646 227792 569001 032898 089248 > 8¹⁷³ [i]