MinT - Best Known (11, 82, s)-Nets in Base 8

Best Known (11, 82, s)-Nets in Base 8

(11, 82, 48)-Net over F₈ — Constructive and digital

Digital (11, 82, 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]

(11, 82, 96)-Net in Base 8 — Upper bound on s

There is no (11, 82, 97)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁸², 97, S₈, 71), but
- the linear programming bound shows that MÂ â‰¥ 58444 451122 976054 015631 654740 532703 876413 511021 390906 807258 676803 077207 110626 024764 735488 / 479 021865 927165 > 8⁸² [i]