MinT - Best Known (164, 164+34, s)-Nets in Base 4

Best Known (164, 164+34, s)-Nets in Base 4

(164, 164+34, 1539)-Net over F₄ — Constructive and digital

Digital (164, 198, 1539)-net over F₄, using

6 times m-reduction [i] based on digital (164, 204, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 68, 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]

(164, 164+34, 17988)-Net over F₄ — Digital

Digital (164, 198, 17988)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 164+34, large)-Net in Base 4 — Upper bound on s

There is no (164, 198, large)-net in base 4, because

32 times m-reduction [i] would yield (164, 166, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]