MinT - Best Known (130−54, 130, s)-Nets in Base 9

Best Known (130−54, 130, s)-Nets in Base 9

(130−54, 130, 344)-Net over F₉ — Constructive and digital

Digital (76, 130, 344)-net over F₉, using

8 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]

(130−54, 130, 563)-Net over F₉ — Digital

Digital (76, 130, 563)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−54, 130, 53664)-Net in Base 9 — Upper bound on s

There is no (76, 130, 53665)-net in base 9, because

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]