MinT - Best Known (210−64, 210, s)-Nets in Base 3

Best Known (210−64, 210, s)-Nets in Base 3

(210−64, 210, 228)-Net over F₃ — Constructive and digital

Digital (146, 210, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 70, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(210−64, 210, 440)-Net over F₃ — Digital

Digital (146, 210, 440)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−64, 210, 8617)-Net in Base 3 — Upper bound on s

There is no (146, 210, 8618)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15718 943335 325536 235759 448068 729424 867824 919547 745497 804233 371171 012204 713482 122625 513059 517105 557313 > 3²¹⁰ [i]