MinT - Best Known (69−60, 69, s)-Nets in Base 8

Best Known (69−60, 69, s)-Nets in Base 8

(69−60, 69, 45)-Net over F₈ — Constructive and digital

Digital (9, 69, 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]

(69−60, 69, 85)-Net in Base 8 — Upper bound on s

There is no (9, 69, 86)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁶⁹, 86, S₈, 60), but
- the linear programming bound shows that MÂ â‰¥ 1 629266 293413 620999 969387 163071 049522 367902 457911 246595 278216 646116 339154 419712 / 6446 662510 997709 > 8⁶⁹ [i]