MinT - Best Known (153−33, 153, s)-Nets in Base 3

Best Known (153−33, 153, s)-Nets in Base 3

(153−33, 153, 640)-Net over F₃ — Constructive and digital

Digital (120, 153, 640)-net over F₃, using

3¹ times duplication [i] based on digital (119, 152, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 38, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(153−33, 153, 1238)-Net over F₃ — Digital

Digital (120, 153, 1238)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−33, 153, 115905)-Net in Base 3 — Upper bound on s

There is no (120, 153, 115906)-net in base 3, because

1 times m-reduction [i] would yield (120, 152, 115906)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 330306 152371 440559 264184 030212 443891 476378 178725 515558 806897 020742 311073 > 3¹⁵² [i]