MinT - Best Known (7, 7+41, s)-Nets in Base 8

Best Known (7, 7+41, s)-Nets in Base 8

(7, 7+41, 34)-Net over F₈ — Constructive and digital

Digital (7, 48, 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+41, 112)-Net in Base 8 — Upper bound on s

There is no (7, 48, 113)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁴⁸, 113, S₈, 41), but
- the linear programming bound shows that MÂ â‰¥ 15628 126917 185907 491956 135182 978289 111945 756953 429147 394387 777228 534342 798051 042730 035485 081600 / 687 247396 298160 931015 716756 543768 189388 106353 278083 > 8⁴⁸ [i]