MinT - Best Known (221−91, 221, s)-Nets in Base 3

Best Known (221−91, 221, s)-Nets in Base 3

(221−91, 221, 148)-Net over F₃ — Constructive and digital

Digital (130, 221, 148)-net over F₃, using

5 times m-reduction [i] based on digital (130, 226, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 113, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(221−91, 221, 188)-Net over F₃ — Digital

Digital (130, 221, 188)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−91, 221, 1851)-Net in Base 3 — Upper bound on s

There is no (130, 221, 1852)-net in base 3, because

1 times m-reduction [i] would yield (130, 220, 1852)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 937 521962 819514 918460 084386 440119 901002 717624 580453 886437 130119 466650 449579 674546 976699 511268 243681 375321 > 3²²⁰ [i]