MinT - Best Known (41, 64, s)-Nets in Base 4

Best Known (41, 64, s)-Nets in Base 4

(41, 64, 130)-Net over F₄ — Constructive and digital

Digital (41, 64, 130)-net over F₄, using

6 times m-reduction [i] based on digital (41, 70, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 35, 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]

(41, 64, 172)-Net over F₄ — Digital

Digital (41, 64, 172)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(41, 64, 4583)-Net in Base 4 — Upper bound on s

There is no (41, 64, 4584)-net in base 4, because

1 times m-reduction [i] would yield (41, 63, 4584)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 85 091387 183318 179203 608076 926655 181420 > 4⁶³ [i]