MinT - Best Known (7, 7+49, s)-Nets in Base 8

Best Known (7, 7+49, s)-Nets in Base 8

(7, 7+49, 34)-Net over F₈ — Constructive and digital

Digital (7, 56, 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+49, 75)-Net in Base 8 — Upper bound on s

There is no (7, 56, 76)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁶, 76, S₈, 49), but
- the linear programming bound shows that MÂ â‰¥ 32 955577 896244 859953 243293 036429 490556 030552 787906 407509 421283 344384 / 80736 180137 773875 > 8⁵⁶ [i]