MinT - Best Known (8, 8+13, s)-Nets in Base 3

Best Known (8, 8+13, s)-Nets in Base 3

(8, 8+13, 16)-Net over F₃ — Constructive and digital

Digital (8, 21, 16)-net over F₃, using

t-expansion [i] based on digital (7, 21, 16)-net over F₃, using
- net from sequence [i] based on digital (7, 15)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 7 and N(F) ≥ 16, using
    - an explicitly constructive algebraic function field [i]

(8, 8+13, 17)-Net over F₃ — Digital

Digital (8, 21, 17)-net over F₃, using

net from sequence [i] based on digital (8, 16)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 8 and N(F) ≥ 17, using
  - a curve from the manYPoints database [i]

(8, 8+13, 53)-Net in Base 3 — Upper bound on s

There is no (8, 21, 54)-net in base 3, because

1 times m-reduction [i] would yield (8, 20, 54)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3862 771957 > 3²⁰ [i]