MinT - Best Known (31, 31+109, s)-Nets in Base 8

Best Known (31, 31+109, s)-Nets in Base 8

(31, 31+109, 65)-Net over F₈ — Constructive and digital

Digital (31, 140, 65)-net over F₈, using

t-expansion [i] based on digital (14, 140, 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+109, 97)-Net over F₈ — Digital

Digital (31, 140, 97)-net over F₈, using

t-expansion [i] based on digital (28, 140, 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+109, 598)-Net in Base 8 — Upper bound on s

There is no (31, 140, 599)-net in base 8, because

1 times m-reduction [i] would yield (31, 139, 599)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 343066 117753 375254 197552 619302 543145 512725 962909 796548 327279 090330 241112 727783 741550 355959 081715 416238 406319 310859 285988 423826 > 8¹³⁹ [i]