MinT - Best Known (39, 39+21, s)-Nets in Base 4

Best Known (39, 39+21, s)-Nets in Base 4

(39, 39+21, 130)-Net over F₄ — Constructive and digital

Digital (39, 60, 130)-net over F₄, using

6 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+21, 184)-Net over F₄ — Digital

Digital (39, 60, 184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+21, 5374)-Net in Base 4 — Upper bound on s

There is no (39, 60, 5375)-net in base 4, because

1 times m-reduction [i] would yield (39, 59, 5375)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 332319 045679 585321 309868 201076 902851 > 4⁵⁹ [i]