MinT - Best Known (31, 31+81, s)-Nets in Base 8

Best Known (31, 31+81, s)-Nets in Base 8

(31, 31+81, 65)-Net over F₈ — Constructive and digital

Digital (31, 112, 65)-net over F₈, using

t-expansion [i] based on digital (14, 112, 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+81, 97)-Net over F₈ — Digital

Digital (31, 112, 97)-net over F₈, using

t-expansion [i] based on digital (28, 112, 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+81, 697)-Net in Base 8 — Upper bound on s

There is no (31, 112, 698)-net in base 8, because

1 times m-reduction [i] would yield (31, 111, 698)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18055 224309 861597 927705 870057 111529 059537 171485 564961 464051 119293 678542 116030 124910 953493 792052 021677 > 8¹¹¹ [i]