MinT - Best Known (176−77, 176, s)-Nets in Base 4

Best Known (176−77, 176, s)-Nets in Base 4

(176−77, 176, 130)-Net over F₄ — Constructive and digital

Digital (99, 176, 130)-net over F₄, using

10 times m-reduction [i] based on digital (99, 186, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 93, 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]

(176−77, 176, 196)-Net over F₄ — Digital

Digital (99, 176, 196)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−77, 176, 2936)-Net in Base 4 — Upper bound on s

There is no (99, 176, 2937)-net in base 4, because

1 times m-reduction [i] would yield (99, 175, 2937)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2322 458359 917666 839850 715457 875024 184483 121933 102932 264067 747712 711728 867975 514685 000747 871029 729391 107860 > 4¹⁷⁵ [i]