MinT - Best Known (111, 145, s)-Nets in Base 9

Best Known (111, 145, s)-Nets in Base 9

(111, 145, 1460)-Net over F₉ — Constructive and digital

Digital (111, 145, 1460)-net over F₉, using

5 times m-reduction [i] based on digital (111, 150, 1460)-net over F₉, using
- trace code for nets [i] based on digital (36, 75, 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]

(111, 145, 25670)-Net over F₉ — Digital

Digital (111, 145, 25670)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 145, large)-Net in Base 9 — Upper bound on s

There is no (111, 145, large)-net in base 9, because

32 times m-reduction [i] would yield (111, 113, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]