MinT - Best Known (44, 44+31, s)-Nets in Base 4

Best Known (44, 44+31, s)-Nets in Base 4

(44, 44+31, 130)-Net over F₄ — Constructive and digital

Digital (44, 75, 130)-net over F₄, using

1 times m-reduction [i] based on digital (44, 76, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 38, 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]

(44, 44+31, 1987)-Net in Base 4 — Upper bound on s

There is no (44, 75, 1988)-net in base 4, because

1 times m-reduction [i] would yield (44, 74, 1988)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 359 482881 253676 670495 162519 297494 197603 553200 > 4⁷⁴ [i]