MinT - Best Known (152, 152+75, s)-Nets in Base 3

Best Known (152, 152+75, s)-Nets in Base 3

(152, 152+75, 162)-Net over F₃ — Constructive and digital

Digital (152, 227, 162)-net over F₃, using

13 times m-reduction [i] based on digital (152, 240, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 120, 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]

(152, 152+75, 365)-Net over F₃ — Digital

Digital (152, 227, 365)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 152+75, 5977)-Net in Base 3 — Upper bound on s

There is no (152, 227, 5978)-net in base 3, because

1 times m-reduction [i] would yield (152, 226, 5978)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 675319 352675 932953 653380 067081 057874 339651 320340 633376 307738 242795 385087 448956 233637 284134 193128 253806 073933 > 3²²⁶ [i]