MinT - Best Known (144−34, 144, s)-Nets in Base 9

Best Known (144−34, 144, s)-Nets in Base 9

(144−34, 144, 1460)-Net over F₉ — Constructive and digital

Digital (110, 144, 1460)-net over F₉, using

4 times m-reduction [i] based on digital (110, 148, 1460)-net over F₉, using
- trace code for nets [i] based on digital (36, 74, 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]

(144−34, 144, 24017)-Net over F₉ — Digital

Digital (110, 144, 24017)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−34, 144, large)-Net in Base 9 — Upper bound on s

There is no (110, 144, large)-net in base 9, because

32 times m-reduction [i] would yield (110, 112, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]