MinT - Best Known (127−39, 127, s)-Nets in Base 9

Best Known (127−39, 127, s)-Nets in Base 9

(127−39, 127, 740)-Net over F₉ — Constructive and digital

Digital (88, 127, 740)-net over F₉, using

17 times m-reduction [i] based on digital (88, 144, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 72, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(127−39, 127, 2922)-Net over F₉ — Digital

Digital (88, 127, 2922)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−39, 127, 2109879)-Net in Base 9 — Upper bound on s

There is no (88, 127, 2109880)-net in base 9, because

1 times m-reduction [i] would yield (88, 126, 2109880)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 716156 820055 333214 988678 028043 837427 258772 653311 540644 037743 072307 525109 119769 584195 611198 630302 697611 216851 279181 064769 > 9¹²⁶ [i]