MinT - Best Known (52−34, 52, s)-Nets in Base 3

Best Known (52−34, 52, s)-Nets in Base 3

(52−34, 52, 28)-Net over F₃ — Constructive and digital

Digital (18, 52, 28)-net over F₃, using

t-expansion [i] based on digital (15, 52, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(52−34, 52, 71)-Net in Base 3 — Upper bound on s

There is no (18, 52, 72)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁵², 72, S₃, 34), but
- the linear programming bound shows that MÂ â‰¥ 23373 085764 731132 483065 978750 735767 / 2987 457005 > 3⁵² [i]