MinT - Best Known (1, 1+4, s)-Nets in Base 8

Best Known (1, 1+4, s)-Nets in Base 8

(1, 1+4, 14)-Net over F₈ — Constructive and digital

Digital (1, 5, 14)-net over F₈, using

net from sequence [i] based on digital (1, 13)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
  - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(1, 1+4, 34)-Net in Base 8 — Upper bound on s

There is no (1, 5, 35)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵, 35, S₈, 4), but
- the linear programming bound shows that MÂ â‰¥ 1 306624 / 39 > 8⁵ [i]