MinT - Best Known (152−42, 152, s)-Nets in Base 3

Best Known (152−42, 152, s)-Nets in Base 3

(152−42, 152, 252)-Net over F₃ — Constructive and digital

Digital (110, 152, 252)-net over F₃, using

1 times m-reduction [i] based on digital (110, 153, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 51, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(152−42, 152, 466)-Net over F₃ — Digital

Digital (110, 152, 466)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−42, 152, 12308)-Net in Base 3 — Upper bound on s

There is no (110, 152, 12309)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 335264 045917 762731 891585 561100 585857 097996 025775 847636 629528 668767 744763 > 3¹⁵² [i]