MinT - Best Known (43−19, 43, s)-Nets in Base 3

Best Known (43−19, 43, s)-Nets in Base 3

(43−19, 43, 40)-Net over F₃ — Constructive and digital

Digital (24, 43, 40)-net over F₃, using

1 times m-reduction [i] based on digital (24, 44, 40)-net over F₃, using
- trace code for nets [i] based on digital (2, 22, 20)-net over F₉, using
  - net from sequence [i] based on digital (2, 19)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
      - a function field by GarcÃa and Quoos [i]

(43−19, 43, 45)-Net over F₃ — Digital

Digital (24, 43, 45)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(43−19, 43, 340)-Net in Base 3 — Upper bound on s

There is no (24, 43, 341)-net in base 3, because

1 times m-reduction [i] would yield (24, 42, 341)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 109 539785 294380 670219 > 3⁴² [i]