MinT - Best Known (21, 37, s)-Nets in Base 4

Best Known (21, 37, s)-Nets in Base 4

(21, 37, 66)-Net over F₄ — Constructive and digital

Digital (21, 37, 66)-net over F₄, using

1 times m-reduction [i] based on digital (21, 38, 66)-net over F₄, using
- trace code for nets [i] based on digital (2, 19, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]

(21, 37, 757)-Net in Base 4 — Upper bound on s

There is no (21, 37, 758)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 18917 549958 959336 053390 > 4³⁷ [i]