MinT - Best Known (243−48, 243, s)-Nets in Base 3

Best Known (243−48, 243, s)-Nets in Base 3

(243−48, 243, 688)-Net over F₃ — Constructive and digital

Digital (195, 243, 688)-net over F₃, using

t-expansion [i] based on digital (193, 243, 688)-net over F₃, using
- 5 times m-reduction [i] based on digital (193, 248, 688)-net over F₃, using
  - trace code for nets [i] based on digital (7, 62, 172)-net over F₈₁, using
    - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
        a function field by SÃ©mirat [i]

(243−48, 243, 2714)-Net over F₃ — Digital

Digital (195, 243, 2714)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−48, 243, 332012)-Net in Base 3 — Upper bound on s

There is no (195, 243, 332013)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 191481 984815 920426 602975 584342 815065 929047 034432 548186 228043 867034 065879 679425 509164 177112 889269 122589 414219 193121 > 3²⁴³ [i]