MinT - Best Known (60−47, 60, s)-Nets in Base 8

Best Known (60−47, 60, s)-Nets in Base 8

(60−47, 60, 48)-Net over F₈ — Constructive and digital

Digital (13, 60, 48)-net over F₈, using

t-expansion [i] based on digital (11, 60, 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]

(60−47, 60, 56)-Net over F₈ — Digital

Digital (13, 60, 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]

(60−47, 60, 253)-Net in Base 8 — Upper bound on s

There is no (13, 60, 254)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁶⁰, 254, S₈, 47), but
- the linear programming bound shows that MÂ â‰¥ 3032 209016 893310 953960 941748 646642 438569 879441 680656 449888 407048 151652 721785 128460 355067 548902 599013 932393 768142 789148 672000 / 1899 299327 526521 237694 686345 650282 604236 970883 363228 316461 841111 706267 > 8⁶⁰ [i]