MinT - Best Known (58, 58+91, s)-Nets in Base 3

Best Known (58, 58+91, s)-Nets in Base 3

(58, 58+91, 48)-Net over F₃ — Constructive and digital

Digital (58, 149, 48)-net over F₃, using

t-expansion [i] based on digital (45, 149, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(58, 58+91, 64)-Net over F₃ — Digital

Digital (58, 149, 64)-net over F₃, using

t-expansion [i] based on digital (49, 149, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(58, 58+91, 284)-Net in Base 3 — Upper bound on s

There is no (58, 149, 285)-net in base 3, because

1 times m-reduction [i] would yield (58, 148, 285)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 42860 209750 472576 051712 676247 019073 665295 715510 965288 609184 130187 753515 > 3¹⁴⁸ [i]