MinT - Best Known (13, 13+82, s)-Nets in Base 8

Best Known (13, 13+82, s)-Nets in Base 8

(13, 13+82, 48)-Net over F₈ — Constructive and digital

Digital (13, 95, 48)-net over F₈, using

t-expansion [i] based on digital (11, 95, 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+82, 56)-Net over F₈ — Digital

Digital (13, 95, 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+82, 111)-Net in Base 8 — Upper bound on s

There is no (13, 95, 112)-net in base 8, because

1 times m-reduction [i] would yield (13, 94, 112)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8⁹⁴, 112, S₈, 81), but
  - the linear programming bound shows that MÂ â‰¥ 5280 498181 820313 025492 202011 550986 058048 893359 230935 825075 234051 428177 087565 066338 664628 133746 966528 / 529 598634 353685 > 8⁹⁴ [i]