MinT - Best Known (142−45, 142, s)-Nets in Base 3

Best Known (142−45, 142, s)-Nets in Base 3

(142−45, 142, 156)-Net over F₃ — Constructive and digital

Digital (97, 142, 156)-net over F₃, using

8 times m-reduction [i] based on digital (97, 150, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 75, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(142−45, 142, 279)-Net over F₃ — Digital

Digital (97, 142, 279)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−45, 142, 5151)-Net in Base 3 — Upper bound on s

There is no (97, 142, 5152)-net in base 3, because

1 times m-reduction [i] would yield (97, 141, 5152)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 840065 807025 870591 929208 962378 844039 346979 637209 532405 060801 149121 > 3¹⁴¹ [i]