MinT - Best Known (227−99, 227, s)-Nets in Base 3

Best Known (227−99, 227, s)-Nets in Base 3

(227−99, 227, 128)-Net over F₃ — Constructive and digital

Digital (128, 227, 128)-net over F₃, using

3 times m-reduction [i] based on digital (128, 230, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 115, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(227−99, 227, 164)-Net over F₃ — Digital

Digital (128, 227, 164)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−99, 227, 1468)-Net in Base 3 — Upper bound on s

There is no (128, 227, 1469)-net in base 3, because

1 times m-reduction [i] would yield (128, 226, 1469)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 680383 958266 302076 538011 191410 514733 124299 344746 555927 603889 416600 529546 976612 005711 639577 674133 006228 400571 > 3²²⁶ [i]