MinT - Best Known (164−151, 164, s)-Nets in Base 8

Best Known (164−151, 164, s)-Nets in Base 8

(164−151, 164, 48)-Net over F₈ — Constructive and digital

Digital (13, 164, 48)-net over F₈, using

t-expansion [i] based on digital (11, 164, 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]

(164−151, 164, 56)-Net over F₈ — Digital

Digital (13, 164, 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]

(164−151, 164, 109)-Net in Base 8 — Upper bound on s

There is no (13, 164, 110)-net in base 8, because

67 times m-reduction [i] would yield (13, 97, 110)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8⁹⁷, 110, S₈, 84), but
  - the linear programming bound shows that MÂ â‰¥ 87 442260 579156 872329 556537 484049 482232 625246 743955 766998 590856 788306 377700 670838 673713 994659 790848 / 17229 021875 > 8⁹⁷ [i]