MinT - Best Known (140−56, 140, s)-Nets in Base 4

Best Known (140−56, 140, s)-Nets in Base 4

(140−56, 140, 130)-Net over F₄ — Constructive and digital

Digital (84, 140, 130)-net over F₄, using

16 times m-reduction [i] based on digital (84, 156, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 78, 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]

(140−56, 140, 216)-Net over F₄ — Digital

Digital (84, 140, 216)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−56, 140, 3833)-Net in Base 4 — Upper bound on s

There is no (84, 140, 3834)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 947848 721220 013341 579008 473175 537601 534392 032391 135712 134650 828180 483792 948279 269576 > 4¹⁴⁰ [i]