MinT - Best Known (72−26, 72, s)-Nets in Base 4

Best Known (72−26, 72, s)-Nets in Base 4

(72−26, 72, 130)-Net over F₄ — Constructive and digital

Digital (46, 72, 130)-net over F₄, using

8 times m-reduction [i] based on digital (46, 80, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 40, 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]

(72−26, 72, 183)-Net over F₄ — Digital

Digital (46, 72, 183)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−26, 72, 4070)-Net in Base 4 — Upper bound on s

There is no (46, 72, 4071)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 22 320748 322969 434493 757040 376698 681614 184264 > 4⁷² [i]