MinT - Best Known (63−41, 63, s)-Nets in Base 3

Best Known (63−41, 63, s)-Nets in Base 3

(63−41, 63, 32)-Net over F₃ — Constructive and digital

Digital (22, 63, 32)-net over F₃, using

t-expansion [i] based on digital (21, 63, 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]

(63−41, 63, 80)-Net in Base 3 — Upper bound on s

There is no (22, 63, 81)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶³, 81, S₃, 41), but
- the linear programming bound shows that MÂ â‰¥ 645814 120288 256333 139417 572410 149042 / 494527 > 3⁶³ [i]