MinT - Best Known (175, 175+59, s)-Nets in Base 3

Best Known (175, 175+59, s)-Nets in Base 3

(175, 175+59, 324)-Net over F₃ — Constructive and digital

Digital (175, 234, 324)-net over F₃, using

t-expansion [i] based on digital (174, 234, 324)-net over F₃, using
- trace code for nets [i] based on digital (18, 78, 108)-net over F₂₇, using
  - net from sequence [i] based on digital (18, 107)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 108, using
      - F₃ from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F₂₇ [i]

(175, 175+59, 936)-Net over F₃ — Digital

Digital (175, 234, 936)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 175+59, 39737)-Net in Base 3 — Upper bound on s

There is no (175, 234, 39738)-net in base 3, because

1 times m-reduction [i] would yield (175, 233, 39738)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1476 835235 553861 782155 805777 741719 941000 492121 658513 693979 557911 495225 663618 099258 032207 671410 937383 946671 573469 > 3²³³ [i]