MinT - Best Known (227−97, 227, s)-Nets in Base 3

Best Known (227−97, 227, s)-Nets in Base 3

(227−97, 227, 128)-Net over F₃ — Constructive and digital

Digital (130, 227, 128)-net over F₃, using

7 times m-reduction [i] based on digital (130, 234, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 117, 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]

(227−97, 227, 173)-Net over F₃ — Digital

Digital (130, 227, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−97, 227, 1605)-Net in Base 3 — Upper bound on s

There is no (130, 227, 1606)-net in base 3, because

1 times m-reduction [i] would yield (130, 226, 1606)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 678989 853459 482661 276814 271829 226543 157384 599840 493124 987767 915262 083006 320949 913323 093131 612125 510599 311329 > 3²²⁶ [i]