MinT - Best Known (160−65, 160, s)-Nets in Base 4

Best Known (160−65, 160, s)-Nets in Base 4

(160−65, 160, 130)-Net over F₄ — Constructive and digital

Digital (95, 160, 130)-net over F₄, using

18 times m-reduction [i] based on digital (95, 178, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 89, 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]

(160−65, 160, 229)-Net over F₄ — Digital

Digital (95, 160, 229)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−65, 160, 4154)-Net in Base 4 — Upper bound on s

There is no (95, 160, 4155)-net in base 4, because

1 times m-reduction [i] would yield (95, 159, 4155)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 535820 479486 055044 999149 031595 040141 612692 383585 311161 783119 257675 378435 478070 049304 545048 838603 > 4¹⁵⁹ [i]