MinT - Best Known (31, 152, s)-Nets in Base 8

Best Known (31, 152, s)-Nets in Base 8

(31, 152, 65)-Net over F₈ — Constructive and digital

Digital (31, 152, 65)-net over F₈, using

t-expansion [i] based on digital (14, 152, 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, 152, 97)-Net over F₈ — Digital

Digital (31, 152, 97)-net over F₈, using

t-expansion [i] based on digital (28, 152, 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, 152, 583)-Net in Base 8 — Upper bound on s

There is no (31, 152, 584)-net in base 8, because

1 times m-reduction [i] would yield (31, 151, 584)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 24392 479336 175747 074296 432665 712254 621606 318821 727830 336921 926239 543776 091929 620648 271731 256952 281701 178279 931157 236259 432551 760482 897752 > 8¹⁵¹ [i]