MinT - Best Known (248−97, 248, s)-Nets in Base 3

Best Known (248−97, 248, s)-Nets in Base 3

(248−97, 248, 156)-Net over F₃ — Constructive and digital

Digital (151, 248, 156)-net over F₃, using

t-expansion [i] based on digital (147, 248, 156)-net over F₃, using
- 2 times m-reduction [i] based on digital (147, 250, 156)-net over F₃, using
  - trace code for nets [i] based on digital (22, 125, 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]

(248−97, 248, 240)-Net over F₃ — Digital

Digital (151, 248, 240)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−97, 248, 2625)-Net in Base 3 — Upper bound on s

There is no (151, 248, 2626)-net in base 3, because

1 times m-reduction [i] would yield (151, 247, 2626)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7122 953203 484001 615955 627499 368033 812608 705442 879193 745796 414975 447525 896656 621707 639551 614136 762312 481575 401929 958881 > 3²⁴⁷ [i]