MinT - Best Known (108, 108+44, s)-Nets in Base 3

Best Known (108, 108+44, s)-Nets in Base 3

(108, 108+44, 228)-Net over F₃ — Constructive and digital

Digital (108, 152, 228)-net over F₃, using

1 times m-reduction [i] based on digital (108, 153, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 51, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(108, 108+44, 396)-Net over F₃ — Digital

Digital (108, 152, 396)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+44, 8938)-Net in Base 3 — Upper bound on s

There is no (108, 152, 8939)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 335644 069983 611430 313089 674652 375163 118088 872288 263142 722144 425755 054733 > 3¹⁵² [i]