MinT - Best Known (66−44, 66, s)-Nets in Base 3

Best Known (66−44, 66, s)-Nets in Base 3

(66−44, 66, 32)-Net over F₃ — Constructive and digital

Digital (22, 66, 32)-net over F₃, using

t-expansion [i] based on digital (21, 66, 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]

(66−44, 66, 76)-Net in Base 3 — Upper bound on s

There is no (22, 66, 77)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶⁶, 77, S₃, 44), but
- the linear programming bound shows that MÂ â‰¥ 34 245670 463812 538347 598340 341640 500169 / 1 016275 > 3⁶⁶ [i]