MinT - Best Known (107−71, 107, s)-Nets in Base 8

Best Known (107−71, 107, s)-Nets in Base 8

(107−71, 107, 65)-Net over F₈ — Constructive and digital

Digital (36, 107, 65)-net over F₈, using

t-expansion [i] based on digital (14, 107, 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]

(107−71, 107, 112)-Net over F₈ — Digital

Digital (36, 107, 112)-net over F₈, using

t-expansion [i] based on digital (35, 107, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(107−71, 107, 1057)-Net in Base 8 — Upper bound on s

There is no (36, 107, 1058)-net in base 8, because

1 times m-reduction [i] would yield (36, 106, 1058)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 539654 184170 947129 631288 923478 310817 593133 163308 500219 727817 845831 746109 470765 840905 005889 913152 > 8¹⁰⁶ [i]