MinT - Best Known (52, 81, s)-Nets in Base 4

Best Known (52, 81, s)-Nets in Base 4

(52, 81, 130)-Net over F₄ — Constructive and digital

Digital (52, 81, 130)-net over F₄, using

11 times m-reduction [i] based on digital (52, 92, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 46, 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]

(52, 81, 205)-Net over F₄ — Digital

Digital (52, 81, 205)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 81, 5543)-Net in Base 4 — Upper bound on s

There is no (52, 81, 5544)-net in base 4, because

1 times m-reduction [i] would yield (52, 80, 5544)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 462308 347921 054709 768460 561963 264026 523145 856220 > 4⁸⁰ [i]