MinT - Best Known (63−24, 63, s)-Nets in Base 4

Best Known (63−24, 63, s)-Nets in Base 4

(63−24, 63, 130)-Net over F₄ — Constructive and digital

Digital (39, 63, 130)-net over F₄, using

3 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]

(63−24, 63, 137)-Net over F₄ — Digital

Digital (39, 63, 137)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(63−24, 63, 2543)-Net in Base 4 — Upper bound on s

There is no (39, 63, 2544)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 85 255083 066701 144383 910122 806699 365755 > 4⁶³ [i]