MinT - Best Known (53−22, 53, s)-Nets in Base 4

Best Known (53−22, 53, s)-Nets in Base 4

(53−22, 53, 90)-Net over F₄ — Constructive and digital

Digital (31, 53, 90)-net over F₄, using

1 times m-reduction [i] based on digital (31, 54, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 27, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(53−22, 53, 91)-Net over F₄ — Digital

Digital (31, 53, 91)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(53−22, 53, 1293)-Net in Base 4 — Upper bound on s

There is no (31, 53, 1294)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 81 332056 898517 305661 503370 701650 > 4⁵³ [i]