MinT - Best Known (65, 65+85, s)-Nets in Base 3

Best Known (65, 65+85, s)-Nets in Base 3

(65, 65+85, 48)-Net over F₃ — Constructive and digital

Digital (65, 150, 48)-net over F₃, using

t-expansion [i] based on digital (45, 150, 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]

(65, 65+85, 64)-Net over F₃ — Digital

Digital (65, 150, 64)-net over F₃, using

t-expansion [i] based on digital (49, 150, 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]

(65, 65+85, 367)-Net in Base 3 — Upper bound on s

There is no (65, 150, 368)-net in base 3, because

1 times m-reduction [i] would yield (65, 149, 368)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 136691 080330 753773 925845 897161 788862 886152 609032 346787 761304 090161 978785 > 3¹⁴⁹ [i]