MinT - Best Known (125, 125+57, s)-Nets in Base 3

Best Known (125, 125+57, s)-Nets in Base 3

(125, 125+57, 162)-Net over F₃ — Constructive and digital

Digital (125, 182, 162)-net over F₃, using

4 times m-reduction [i] based on digital (125, 186, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 93, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(125, 125+57, 357)-Net over F₃ — Digital

Digital (125, 182, 357)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 125+57, 6830)-Net in Base 3 — Upper bound on s

There is no (125, 182, 6831)-net in base 3, because

1 times m-reduction [i] would yield (125, 181, 6831)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 577522 125675 821600 135859 855226 630736 400411 615559 771298 975750 112197 717570 351800 254153 > 3¹⁸¹ [i]