MinT - Best Known (52, 52+24, s)-Nets in Base 4

Best Known (52, 52+24, s)-Nets in Base 4

(52, 52+24, 240)-Net over F₄ — Constructive and digital

Digital (52, 76, 240)-net over F₄, using

4¹ times duplication [i] based on digital (51, 75, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 25, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(52, 52+24, 318)-Net over F₄ — Digital

Digital (52, 76, 318)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+24, 11453)-Net in Base 4 — Upper bound on s

There is no (52, 76, 11454)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5713 780035 634394 019690 754975 178657 031868 383715 > 4⁷⁶ [i]