MinT - Best Known (174−53, 174, s)-Nets in Base 3

Best Known (174−53, 174, s)-Nets in Base 3

(174−53, 174, 204)-Net over F₃ — Constructive and digital

Digital (121, 174, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 58, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(174−53, 174, 374)-Net over F₃ — Digital

Digital (121, 174, 374)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−53, 174, 7862)-Net in Base 3 — Upper bound on s

There is no (121, 174, 7863)-net in base 3, because

1 times m-reduction [i] would yield (121, 173, 7863)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34911 362063 527955 513789 821199 971586 249545 027474 329077 898927 024497 826861 137713 356477 > 3¹⁷³ [i]