MinT - Best Known (197−61, 197, s)-Nets in Base 3

Best Known (197−61, 197, s)-Nets in Base 3

(197−61, 197, 192)-Net over F₃ — Constructive and digital

Digital (136, 197, 192)-net over F₃, using

1 times m-reduction [i] based on digital (136, 198, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 66, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(197−61, 197, 396)-Net over F₃ — Digital

Digital (136, 197, 396)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−61, 197, 7858)-Net in Base 3 — Upper bound on s

There is no (136, 197, 7859)-net in base 3, because

1 times m-reduction [i] would yield (136, 196, 7859)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3288 491331 923324 862344 973991 914542 957323 067265 679196 415329 844671 204958 562168 069031 212226 456205 > 3¹⁹⁶ [i]