MinT - Best Known (53, 53+21, s)-Nets in Base 4

Best Known (53, 53+21, s)-Nets in Base 4

(53, 53+21, 312)-Net over F₄ — Constructive and digital

Digital (53, 74, 312)-net over F₄, using

1 times m-reduction [i] based on digital (53, 75, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 25, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(53, 53+21, 477)-Net over F₄ — Digital

Digital (53, 74, 477)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+21, 37480)-Net in Base 4 — Upper bound on s

There is no (53, 74, 37481)-net in base 4, because

1 times m-reduction [i] would yield (53, 73, 37481)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 89 221329 822931 128228 046186 406260 993795 156960 > 4⁷³ [i]