MinT - Best Known (211−81, 211, s)-Nets in Base 3

Best Known (211−81, 211, s)-Nets in Base 3

(211−81, 211, 156)-Net over F₃ — Constructive and digital

Digital (130, 211, 156)-net over F₃, using

5 times m-reduction [i] based on digital (130, 216, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 108, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(211−81, 211, 220)-Net over F₃ — Digital

Digital (130, 211, 220)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−81, 211, 2482)-Net in Base 3 — Upper bound on s

There is no (130, 211, 2483)-net in base 3, because

1 times m-reduction [i] would yield (130, 210, 2483)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15886 867340 275766 019489 938077 121742 496562 197960 105051 586144 911395 333981 684422 821285 291517 776056 346801 > 3²¹⁰ [i]