MinT - Best Known (245−53, 245, s)-Nets in Base 3

Best Known (245−53, 245, s)-Nets in Base 3

(245−53, 245, 688)-Net over F₃ — Constructive and digital

Digital (192, 245, 688)-net over F₃, using

3¹ times duplication [i] based on digital (191, 244, 688)-net over F₃, using
- t-expansion [i] based on digital (190, 244, 688)-net over F₃, using
  - trace code for nets [i] based on digital (7, 61, 172)-net over F₈₁, using
    - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
        a function field by SÃ©mirat [i]

(245−53, 245, 1816)-Net over F₃ — Digital

Digital (192, 245, 1816)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−53, 245, 158413)-Net in Base 3 — Upper bound on s

There is no (192, 245, 158414)-net in base 3, because

1 times m-reduction [i] would yield (192, 244, 158414)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 261 583761 972826 477328 611941 276569 038221 090442 823354 567927 986540 454538 181303 996366 954967 205590 927954 955545 473218 858765 > 3²⁴⁴ [i]