MinT - Best Known (124, 124+47, s)-Nets in Base 3

Best Known (124, 124+47, s)-Nets in Base 3

(124, 124+47, 282)-Net over F₃ — Constructive and digital

Digital (124, 171, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 57, 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]

(124, 124+47, 523)-Net over F₃ — Digital

Digital (124, 171, 523)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+47, 15825)-Net in Base 3 — Upper bound on s

There is no (124, 171, 15826)-net in base 3, because

1 times m-reduction [i] would yield (124, 170, 15826)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1290 966087 211619 682467 949291 559719 511010 701607 097689 160793 385867 236784 942187 109257 > 3¹⁷⁰ [i]