MinT - Best Known (220−63, 220, s)-Nets in Base 3

Best Known (220−63, 220, s)-Nets in Base 3

(220−63, 220, 282)-Net over F₃ — Constructive and digital

Digital (157, 220, 282)-net over F₃, using

3¹ times duplication [i] based on digital (156, 219, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 73, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(220−63, 220, 561)-Net over F₃ — Digital

Digital (157, 220, 561)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−63, 220, 14545)-Net in Base 3 — Upper bound on s

There is no (157, 220, 14546)-net in base 3, because

1 times m-reduction [i] would yield (157, 219, 14546)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 309 125234 788027 980385 279834 232104 031574 679893 297635 725328 178426 994237 865377 200056 364751 795892 875250 398905 > 3²¹⁹ [i]