MinT - Best Known (109−79, 109, s)-Nets in Base 8

Best Known (109−79, 109, s)-Nets in Base 8

(109−79, 109, 65)-Net over F₈ — Constructive and digital

Digital (30, 109, 65)-net over F₈, using

t-expansion [i] based on digital (14, 109, 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]

(109−79, 109, 97)-Net over F₈ — Digital

Digital (30, 109, 97)-net over F₈, using

t-expansion [i] based on digital (28, 109, 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]

(109−79, 109, 672)-Net in Base 8 — Upper bound on s

There is no (30, 109, 673)-net in base 8, because

1 times m-reduction [i] would yield (30, 108, 673)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 34 903664 734618 394615 834372 275524 831084 872680 728004 651765 256095 090847 987332 554356 119229 489277 522560 > 8¹⁰⁸ [i]