MinT - Best Known (132−56, 132, s)-Nets in Base 9

Best Known (132−56, 132, s)-Nets in Base 9

(132−56, 132, 344)-Net over F₉ — Constructive and digital

Digital (76, 132, 344)-net over F₉, using

6 times m-reduction [i] based on digital (76, 138, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 69, 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]

(132−56, 132, 514)-Net over F₉ — Digital

Digital (76, 132, 514)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−56, 132, 44496)-Net in Base 9 — Upper bound on s

There is no (76, 132, 44497)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 912606 774086 717543 471063 081347 976060 406029 584342 373539 064106 205748 098213 405524 810336 988847 382813 639291 327716 738777 195322 665313 > 9¹³² [i]