MinT - Best Known (112, 112+41, s)-Nets in Base 3

Best Known (112, 112+41, s)-Nets in Base 3

(112, 112+41, 282)-Net over F₃ — Constructive and digital

Digital (112, 153, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 51, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(112, 112+41, 525)-Net over F₃ — Digital

Digital (112, 153, 525)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+41, 17535)-Net in Base 3 — Upper bound on s

There is no (112, 153, 17536)-net in base 3, because

1 times m-reduction [i] would yield (112, 152, 17536)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 332229 292336 060600 007029 667906 505288 380569 169088 730220 369968 071002 528769 > 3¹⁵² [i]