MinT - Best Known (13, 62, s)-Nets in Base 8

Best Known (13, 62, s)-Nets in Base 8

(13, 62, 48)-Net over F₈ — Constructive and digital

Digital (13, 62, 48)-net over F₈, using

t-expansion [i] based on digital (11, 62, 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, 62, 56)-Net over F₈ — Digital

Digital (13, 62, 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, 62, 246)-Net in Base 8 — Upper bound on s

There is no (13, 62, 247)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁶², 247, S₈, 49), but
- the linear programming bound shows that MÂ â‰¥ 92 865377 169216 634049 253321 577771 627834 425809 656097 540751 925796 861912 981031 948541 028929 450251 358573 055619 571232 779450 833924 066633 580544 / 944468 297304 525156 446084 540328 287825 391927 974393 550316 998980 503088 512753 629061 > 8⁶² [i]