MinT - Best Known (138−43, 138, s)-Nets in Base 9

Best Known (138−43, 138, s)-Nets in Base 9

(138−43, 138, 740)-Net over F₉ — Constructive and digital

Digital (95, 138, 740)-net over F₉, using

t-expansion [i] based on digital (91, 138, 740)-net over F₉, using
- 12 times m-reduction [i] based on digital (91, 150, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 75, 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]

(138−43, 138, 2840)-Net over F₉ — Digital

Digital (95, 138, 2840)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−43, 138, 1822619)-Net in Base 9 — Upper bound on s

There is no (95, 138, 1822620)-net in base 9, because

1 times m-reduction [i] would yield (95, 137, 1822620)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 53855 213499 180451 913496 375661 661964 864811 077604 289355 497579 569575 119094 264900 648179 069728 977719 716089 692896 852122 654854 241867 391329 > 9¹³⁷ [i]