MinT - Best Known (105−79, 105, s)-Nets in Base 8

Best Known (105−79, 105, s)-Nets in Base 8

(105−79, 105, 65)-Net over F₈ — Constructive and digital

Digital (26, 105, 65)-net over F₈, using

t-expansion [i] based on digital (14, 105, 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]

(105−79, 105, 86)-Net over F₈ — Digital

Digital (26, 105, 86)-net over F₈, using

t-expansion [i] based on digital (25, 105, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(105−79, 105, 538)-Net in Base 8 — Upper bound on s

There is no (26, 105, 539)-net in base 8, because

1 times m-reduction [i] would yield (26, 104, 539)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8444 732012 428672 112136 373181 503020 217320 276633 693943 959001 150912 113125 887825 627574 019498 522240 > 8¹⁰⁴ [i]