MinT - Best Known (126−33, 126, s)-Nets in Base 3

Best Known (126−33, 126, s)-Nets in Base 3

(126−33, 126, 264)-Net over F₃ — Constructive and digital

Digital (93, 126, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 42, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(126−33, 126, 495)-Net over F₃ — Digital

Digital (93, 126, 495)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−33, 126, 18140)-Net in Base 3 — Upper bound on s

There is no (93, 126, 18141)-net in base 3, because

1 times m-reduction [i] would yield (93, 125, 18141)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 436890 257895 262778 402636 000117 177335 055235 162891 885729 358785 > 3¹²⁵ [i]