MinT - Best Known (13, 13+15, s)-Nets in Base 8

Best Known (13, 13+15, s)-Nets in Base 8

(13, 13+15, 48)-Net over F₈ — Constructive and digital

Digital (13, 28, 48)-net over F₈, using

t-expansion [i] based on digital (11, 28, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(13, 13+15, 56)-Net over F₈ — Digital

Digital (13, 28, 56)-net over F₈, using

net from sequence [i] based on digital (13, 55)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 13 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(13, 13+15, 65)-Net in Base 8 — Constructive

(13, 28, 65)-net in base 8, using

base change [i] based on digital (6, 21, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(13, 13+15, 1465)-Net in Base 8 — Upper bound on s

There is no (13, 28, 1466)-net in base 8, because

1 times m-reduction [i] would yield (13, 27, 1466)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 423647 506934 957989 482196 > 8²⁷ [i]