MinT - Best Known (67−23, 67, s)-Nets in Base 4

Best Known (67−23, 67, s)-Nets in Base 4

(67−23, 67, 130)-Net over F₄ — Constructive and digital

Digital (44, 67, 130)-net over F₄, using

9 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]

(67−23, 67, 212)-Net over F₄ — Digital

Digital (44, 67, 212)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(67−23, 67, 6694)-Net in Base 4 — Upper bound on s

There is no (44, 67, 6695)-net in base 4, because

1 times m-reduction [i] would yield (44, 66, 6695)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5452 698440 909141 741274 180767 672870 483680 > 4⁶⁶ [i]