MinT - Best Known (50, 50+51, s)-Nets in Base 3

Best Known (50, 50+51, s)-Nets in Base 3

(50, 50+51, 48)-Net over F₃ — Constructive and digital

Digital (50, 101, 48)-net over F₃, using

t-expansion [i] based on digital (45, 101, 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]

(50, 50+51, 64)-Net over F₃ — Digital

Digital (50, 101, 64)-net over F₃, using

t-expansion [i] based on digital (49, 101, 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]

(50, 50+51, 388)-Net in Base 3 — Upper bound on s

There is no (50, 101, 389)-net in base 3, because

1 times m-reduction [i] would yield (50, 100, 389)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 538918 262828 024902 771810 355846 625305 566993 479723 > 3¹⁰⁰ [i]