MinT - Best Known (9, 52, s)-Nets in Base 8

Best Known (9, 52, s)-Nets in Base 8

(9, 52, 45)-Net over F₈ — Constructive and digital

Digital (9, 52, 45)-net over F₈, using

net from sequence [i] based on digital (9, 44)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
  - an explicitly constructive algebraic function field [i]

(9, 52, 163)-Net in Base 8 — Upper bound on s

There is no (9, 52, 164)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵², 164, S₈, 43), but
- the linear programming bound shows that MÂ â‰¥ 782 273657 658972 919468 089062 689088 927920 714162 274864 444886 623682 836498 087946 013308 579145 235772 211200 / 8287 605185 967441 185206 711800 697780 819279 134039 225209 > 8⁵² [i]