MinT - Best Known (218−49, 218, s)-Nets in Base 3

Best Known (218−49, 218, s)-Nets in Base 3

(218−49, 218, 640)-Net over F₃ — Constructive and digital

Digital (169, 218, 640)-net over F₃, using

3² times duplication [i] based on digital (167, 216, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 54, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(218−49, 218, 1400)-Net over F₃ — Digital

Digital (169, 218, 1400)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−49, 218, 100972)-Net in Base 3 — Upper bound on s

There is no (169, 218, 100973)-net in base 3, because

1 times m-reduction [i] would yield (169, 217, 100973)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 305658 409432 148415 893812 072876 622594 247092 988238 303444 281736 852097 724468 674810 534936 897339 453601 180449 > 3²¹⁷ [i]