MinT - Best Known (62, 62+77, s)-Nets in Base 3

Best Known (62, 62+77, s)-Nets in Base 3

(62, 62+77, 48)-Net over F₃ — Constructive and digital

Digital (62, 139, 48)-net over F₃, using

t-expansion [i] based on digital (45, 139, 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, 62+77, 64)-Net over F₃ — Digital

Digital (62, 139, 64)-net over F₃, using

t-expansion [i] based on digital (49, 139, 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, 62+77, 369)-Net in Base 3 — Upper bound on s

There is no (62, 139, 370)-net in base 3, because

1 times m-reduction [i] would yield (62, 138, 370)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 707382 272079 574538 718143 920446 466734 750045 960268 202979 421024 661277 > 3¹³⁸ [i]