MinT - Best Known (65, 65+78, s)-Nets in Base 3

Best Known (65, 65+78, s)-Nets in Base 3

(65, 65+78, 48)-Net over F₃ — Constructive and digital

Digital (65, 143, 48)-net over F₃, using

t-expansion [i] based on digital (45, 143, 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+78, 64)-Net over F₃ — Digital

Digital (65, 143, 64)-net over F₃, using

t-expansion [i] based on digital (49, 143, 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+78, 395)-Net in Base 3 — Upper bound on s

There is no (65, 143, 396)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 181 555487 085817 412508 793648 448909 535425 341028 491869 636454 923756 008273 > 3¹⁴³ [i]