MinT - Best Known (70−26, 70, s)-Nets in Base 4

Best Known (70−26, 70, s)-Nets in Base 4

(70−26, 70, 130)-Net over F₄ — Constructive and digital

Digital (44, 70, 130)-net over F₄, using

6 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]

(70−26, 70, 161)-Net over F₄ — Digital

Digital (44, 70, 161)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−26, 70, 3286)-Net in Base 4 — Upper bound on s

There is no (44, 70, 3287)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 394413 183086 723938 333554 069117 599754 421164 > 4⁷⁰ [i]