MinT - Best Known (163, 163+34, s)-Nets in Base 4

Best Known (163, 163+34, s)-Nets in Base 4

(163, 163+34, 1539)-Net over F₄ — Constructive and digital

Digital (163, 197, 1539)-net over F₄, using

t-expansion [i] based on digital (162, 197, 1539)-net over F₄, using
- 4 times m-reduction [i] based on digital (162, 201, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 67, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(163, 163+34, 17249)-Net over F₄ — Digital

Digital (163, 197, 17249)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+34, large)-Net in Base 4 — Upper bound on s

There is no (163, 197, large)-net in base 4, because

32 times m-reduction [i] would yield (163, 165, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]