MinT - Best Known (7, 7+31, s)-Nets in Base 8

Best Known (7, 7+31, s)-Nets in Base 8

(7, 7+31, 34)-Net over F₈ — Constructive and digital

Digital (7, 38, 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+31, 144)-Net in Base 8 — Upper bound on s

There is no (7, 38, 145)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8³⁸, 145, S₈, 31), but
- the linear programming bound shows that MÂ â‰¥ 51 042804 306016 116475 500515 468175 689758 584445 178850 379503 532769 280000 / 2368 259365 218364 279296 472650 439703 > 8³⁸ [i]