MinT - Best Known (53−23, 53, s)-Nets in Base 4

Best Known (53−23, 53, s)-Nets in Base 4

(53−23, 53, 76)-Net over F₄ — Constructive and digital

Digital (30, 53, 76)-net over F₄, using

1 times m-reduction [i] based on digital (30, 54, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 27, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(53−23, 53, 79)-Net over F₄ — Digital

Digital (30, 53, 79)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(53−23, 53, 1139)-Net in Base 4 — Upper bound on s

There is no (30, 53, 1140)-net in base 4, because

1 times m-reduction [i] would yield (30, 52, 1140)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 20 380088 091969 831223 427383 263358 > 4⁵² [i]