MinT - Best Known (31, 31+111, s)-Nets in Base 8

Best Known (31, 31+111, s)-Nets in Base 8

(31, 31+111, 65)-Net over F₈ — Constructive and digital

Digital (31, 142, 65)-net over F₈, using

t-expansion [i] based on digital (14, 142, 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+111, 97)-Net over F₈ — Digital

Digital (31, 142, 97)-net over F₈, using

t-expansion [i] based on digital (28, 142, 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+111, 595)-Net in Base 8 — Upper bound on s

There is no (31, 142, 596)-net in base 8, because

1 times m-reduction [i] would yield (31, 141, 596)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 22 452999 638994 991290 645012 618586 810759 976548 145230 162608 477327 749070 710991 734364 700357 630993 352730 437043 768641 931225 869372 243952 > 8¹⁴¹ [i]