MinT - Best Known (62, 137, s)-Nets in Base 3

Best Known (62, 137, s)-Nets in Base 3

(62, 137, 48)-Net over F₃ — Constructive and digital

Digital (62, 137, 48)-net over F₃, using

t-expansion [i] based on digital (45, 137, 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]

(62, 137, 64)-Net over F₃ — Digital

Digital (62, 137, 64)-net over F₃, using

t-expansion [i] based on digital (49, 137, 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]

(62, 137, 380)-Net in Base 3 — Upper bound on s

There is no (62, 137, 381)-net in base 3, because

1 times m-reduction [i] would yield (62, 136, 381)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 82132 544695 597947 646437 536747 034705 763266 774894 667455 580985 681547 > 3¹³⁶ [i]