MinT - Best Known (7, 7+48, s)-Nets in Base 8

Best Known (7, 7+48, s)-Nets in Base 8

(7, 7+48, 34)-Net over F₈ — Constructive and digital

Digital (7, 55, 34)-net over F₈, using

net from sequence [i] based on digital (7, 33)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
  - a function field by SÃ©mirat [i]

(7, 7+48, 78)-Net in Base 8 — Upper bound on s

There is no (7, 55, 79)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁵, 79, S₈, 48), but
- the linear programming bound shows that MÂ â‰¥ 5667 534134 860586 283486 578174 283616 136215 976250 876797 494769 557763 522560 / 115 995702 566521 433799 > 8⁵⁵ [i]