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

Best Known (8−7, 8, s)-Nets in Base 8

(8−7, 8, 14)-Net over F₈ — Constructive and digital

Digital (1, 8, 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]

(8−7, 8, 29)-Net in Base 8 — Upper bound on s

There is no (1, 8, 30)-net in base 8, because

1 times m-reduction [i] would yield (1, 7, 30)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8⁷, 30, S₈, 2, 6), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 659720 765440 / 312937 > 8⁷ [i]