MinT - Best Known (140−32, 140, s)-Nets in Base 9

Best Known (140−32, 140, s)-Nets in Base 9

(140−32, 140, 1460)-Net over F₉ — Constructive and digital

Digital (108, 140, 1460)-net over F₉, using

4 times m-reduction [i] based on digital (108, 144, 1460)-net over F₉, using
- trace code for nets [i] based on digital (36, 72, 730)-net over F₈₁, using
  - net from sequence [i] based on digital (36, 729)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 36 and N(F) ≥ 730, using
      - the Hermitian function field over F₈₁ [i]

(140−32, 140, 31669)-Net over F₉ — Digital

Digital (108, 140, 31669)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−32, 140, large)-Net in Base 9 — Upper bound on s

There is no (108, 140, large)-net in base 9, because

30 times m-reduction [i] would yield (108, 110, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]