MinT - Best Known (131−55, 131, s)-Nets in Base 9

Best Known (131−55, 131, s)-Nets in Base 9

(131−55, 131, 344)-Net over F₉ — Constructive and digital

Digital (76, 131, 344)-net over F₉, using

7 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]

(131−55, 131, 537)-Net over F₉ — Digital

Digital (76, 131, 537)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−55, 131, 53664)-Net in Base 9 — Upper bound on s

There is no (76, 131, 53665)-net in base 9, because

1 times m-reduction [i] would yield (76, 130, 53665)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11263 790919 663708 321358 026445 415536 034219 583037 778578 438379 450511 521870 177507 684477 628272 448394 024655 218685 158493 619522 270617 > 9¹³⁰ [i]