MinT - Best Known (126−37, 126, s)-Nets in Base 3

Best Known (126−37, 126, s)-Nets in Base 3

(126−37, 126, 204)-Net over F₃ — Constructive and digital

Digital (89, 126, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 42, 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]

(126−37, 126, 325)-Net over F₃ — Digital

Digital (89, 126, 325)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−37, 126, 7752)-Net in Base 3 — Upper bound on s

There is no (89, 126, 7753)-net in base 3, because

1 times m-reduction [i] would yield (89, 125, 7753)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 436780 950729 755888 057750 926176 331076 431429 076079 254802 503577 > 3¹²⁵ [i]