MinT - Best Known (149−36, 149, s)-Nets in Base 9

Best Known (149−36, 149, s)-Nets in Base 9

(149−36, 149, 1460)-Net over F₉ — Constructive and digital

Digital (113, 149, 1460)-net over F₉, using

t-expansion [i] based on digital (111, 149, 1460)-net over F₉, using
- 1 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]

(149−36, 149, 20086)-Net over F₉ — Digital

Digital (113, 149, 20086)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−36, 149, large)-Net in Base 9 — Upper bound on s

There is no (113, 149, large)-net in base 9, because

34 times m-reduction [i] would yield (113, 115, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]