MinT - Best Known (72−63, 72, s)-Nets in Base 8

Best Known (72−63, 72, s)-Nets in Base 8

(72−63, 72, 45)-Net over F₈ — Constructive and digital

Digital (9, 72, 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]

(72−63, 72, 81)-Net in Base 8 — Upper bound on s

There is no (9, 72, 82)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁷², 82, S₈, 63), but
- the linear programming bound shows that MÂ â‰¥ 5 943562 882293 362898 492495 479069 260758 679371 222248 872068 611620 811931 910144 / 44 417945 > 8⁷² [i]