MinT - Best Known (52−19, 52, s)-Nets in Base 4

Best Known (52−19, 52, s)-Nets in Base 4

(52−19, 52, 130)-Net over F₄ — Constructive and digital

Digital (33, 52, 130)-net over F₄, using

2 times m-reduction [i] based on digital (33, 54, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 27, 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]

(52−19, 52, 143)-Net over F₄ — Digital

Digital (33, 52, 143)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(52−19, 52, 3560)-Net in Base 4 — Upper bound on s

There is no (33, 52, 3561)-net in base 4, because

1 times m-reduction [i] would yield (33, 51, 3561)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5 083302 332580 970426 998552 563860 > 4⁵¹ [i]