MinT - Best Known (223−65, 223, s)-Nets in Base 3

Best Known (223−65, 223, s)-Nets in Base 3

(223−65, 223, 264)-Net over F₃ — Constructive and digital

Digital (158, 223, 264)-net over F₃, using

3¹ times duplication [i] based on digital (157, 222, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 74, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(223−65, 223, 535)-Net over F₃ — Digital

Digital (158, 223, 535)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−65, 223, 13026)-Net in Base 3 — Upper bound on s

There is no (158, 223, 13027)-net in base 3, because

1 times m-reduction [i] would yield (158, 222, 13027)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8343 336461 479243 599162 599094 599725 626806 338667 914318 306309 205654 796065 961484 391740 582415 103885 103962 490305 > 3²²² [i]