MinT - Best Known (162−45, 162, s)-Nets in Base 3

Best Known (162−45, 162, s)-Nets in Base 3

(162−45, 162, 264)-Net over F₃ — Constructive and digital

Digital (117, 162, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 54, 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]

(162−45, 162, 482)-Net over F₃ — Digital

Digital (117, 162, 482)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−45, 162, 14022)-Net in Base 3 — Upper bound on s

There is no (117, 162, 14023)-net in base 3, because

1 times m-reduction [i] would yield (117, 161, 14023)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65617 875763 460255 255520 877509 173421 557200 643013 946413 012192 562292 067374 708517 > 3¹⁶¹ [i]