MinT - Best Known (176−75, 176, s)-Nets in Base 4

Best Known (176−75, 176, s)-Nets in Base 4

(176−75, 176, 130)-Net over F₄ — Constructive and digital

Digital (101, 176, 130)-net over F₄, using

14 times m-reduction [i] based on digital (101, 190, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 95, 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]

(176−75, 176, 213)-Net over F₄ — Digital

Digital (101, 176, 213)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−75, 176, 3408)-Net in Base 4 — Upper bound on s

There is no (101, 176, 3409)-net in base 4, because

1 times m-reduction [i] would yield (101, 175, 3409)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2311 107808 200551 600063 802950 876871 712787 667670 392179 708844 160124 588464 194335 321329 868691 779999 728684 901440 > 4¹⁷⁵ [i]