MinT - Best Known (12, 12+47, s)-Nets in Base 8

Best Known (12, 12+47, s)-Nets in Base 8

(12, 12+47, 48)-Net over F₈ — Constructive and digital

Digital (12, 59, 48)-net over F₈, using

t-expansion [i] based on digital (11, 59, 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]

(12, 12+47, 49)-Net over F₈ — Digital

Digital (12, 59, 49)-net over F₈, using

net from sequence [i] based on digital (12, 48)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 12 and N(F) ≥ 49, using
  - a curve from the manYPoints database [i]

(12, 12+47, 227)-Net in Base 8 — Upper bound on s

There is no (12, 59, 228)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁹, 228, S₈, 47), but
- the linear programming bound shows that MÂ â‰¥ 4 462800 294451 815489 911426 659069 593398 791085 434676 095530 312228 399832 838195 256782 995332 216724 808281 285028 495746 505113 600000 / 21 108871 835759 357143 956443 533552 074383 643233 187346 935658 076259 759713 > 8⁵⁹ [i]