MinT - Best Known (219−62, 219, s)-Nets in Base 3

Best Known (219−62, 219, s)-Nets in Base 3

(219−62, 219, 288)-Net over F₃ — Constructive and digital

Digital (157, 219, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 73, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(219−62, 219, 580)-Net over F₃ — Digital

Digital (157, 219, 580)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−62, 219, 14545)-Net in Base 3 — Upper bound on s

There is no (157, 219, 14546)-net in base 3, because

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]