MinT - Best Known (39, 39+23, s)-Nets in Base 4

Best Known (39, 39+23, s)-Nets in Base 4

(39, 39+23, 130)-Net over F₄ — Constructive and digital

Digital (39, 62, 130)-net over F₄, using

4 times m-reduction [i] based on digital (39, 66, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 33, 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]

(39, 39+23, 150)-Net over F₄ — Digital

Digital (39, 62, 150)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+23, 3560)-Net in Base 4 — Upper bound on s

There is no (39, 62, 3561)-net in base 4, because

1 times m-reduction [i] would yield (39, 61, 3561)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5 321956 985866 634087 223228 207705 944032 > 4⁶¹ [i]