MinT - Best Known (191−33, 191, s)-Nets in Base 4

Best Known (191−33, 191, s)-Nets in Base 4

(191−33, 191, 1539)-Net over F₄ — Constructive and digital

Digital (158, 191, 1539)-net over F₄, using

4 times m-reduction [i] based on digital (158, 195, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 65, 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]

(191−33, 191, 16738)-Net over F₄ — Digital

Digital (158, 191, 16738)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−33, 191, large)-Net in Base 4 — Upper bound on s

There is no (158, 191, large)-net in base 4, because

31 times m-reduction [i] would yield (158, 160, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]