MinT - Best Known (57−34, 57, s)-Nets in Base 3

Best Known (57−34, 57, s)-Nets in Base 3

(57−34, 57, 32)-Net over F₃ — Constructive and digital

Digital (23, 57, 32)-net over F₃, using

t-expansion [i] based on digital (21, 57, 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]

(57−34, 57, 127)-Net in Base 3 — Upper bound on s

There is no (23, 57, 128)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1761 415636 145532 879084 040449 > 3⁵⁷ [i]