MinT - Best Known (158−69, 158, s)-Nets in Base 4

Best Known (158−69, 158, s)-Nets in Base 4

(158−69, 158, 130)-Net over F₄ — Constructive and digital

Digital (89, 158, 130)-net over F₄, using

8 times m-reduction [i] based on digital (89, 166, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 83, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(158−69, 158, 180)-Net over F₄ — Digital

Digital (89, 158, 180)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−69, 158, 2691)-Net in Base 4 — Upper bound on s

There is no (89, 158, 2692)-net in base 4, because

1 times m-reduction [i] would yield (89, 157, 2692)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 33558 722566 920566 434645 343992 552289 117889 644848 678035 685261 104188 293662 589464 862808 334592 730980 > 4¹⁵⁷ [i]