MinT - Best Known (137−126, 137, s)-Nets in Base 8

Best Known (137−126, 137, s)-Nets in Base 8

(137−126, 137, 48)-Net over F₈ — Constructive and digital

Digital (11, 137, 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]

(137−126, 137, 95)-Net in Base 8 — Upper bound on s

There is no (11, 137, 96)-net in base 8, because

54 times m-reduction [i] would yield (11, 83, 96)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8⁸³, 96, S₈, 72), but
  - the linear programming bound shows that MÂ â‰¥ 601 433997 364031 044137 528178 931541 095128 705181 131547 903349 738124 067793 054941 183723 175936 / 593517 142933 > 8⁸³ [i]