MinT - Best Known (45−25, 45, s)-Nets in Base 3

Best Known (45−25, 45, s)-Nets in Base 3

(45−25, 45, 28)-Net over F₃ — Constructive and digital

Digital (20, 45, 28)-net over F₃, using

t-expansion [i] based on digital (15, 45, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(45−25, 45, 32)-Net over F₃ — Digital

Digital (20, 45, 32)-net over F₃, using

t-expansion [i] based on digital (19, 45, 32)-net over F₃, using
- net from sequence [i] based on digital (19, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 19 and N(F) ≥ 32, using
    - a curve from the manYPoints database [i]

(45−25, 45, 137)-Net in Base 3 — Upper bound on s

There is no (20, 45, 138)-net in base 3, because

1 times m-reduction [i] would yield (20, 44, 138)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1035 678145 224705 006969 > 3⁴⁴ [i]