MinT - Best Known (61−39, 61, s)-Nets in Base 3

Best Known (61−39, 61, s)-Nets in Base 3

(61−39, 61, 32)-Net over F₃ — Constructive and digital

Digital (22, 61, 32)-net over F₃, using

t-expansion [i] based on digital (21, 61, 32)-net over F₃, using
- net from sequence [i] based on digital (21, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]

(61−39, 61, 87)-Net in Base 3 — Upper bound on s

There is no (22, 61, 88)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶¹, 88, S₃, 39), but
- the linear programming bound shows that MÂ â‰¥ 27794 948374 262252 134892 330586 188426 701201 134663 / 193694 611824 634375 > 3⁶¹ [i]