MinT - Best Known (225−73, 225, s)-Nets in Base 4

Best Known (225−73, 225, s)-Nets in Base 4

(225−73, 225, 240)-Net over F₄ — Constructive and digital

Digital (152, 225, 240)-net over F₄, using

t-expansion [i] based on digital (151, 225, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 75, 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]

(225−73, 225, 674)-Net over F₄ — Digital

Digital (152, 225, 674)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−73, 225, 26502)-Net in Base 4 — Upper bound on s

There is no (152, 225, 26503)-net in base 4, because

1 times m-reduction [i] would yield (152, 224, 26503)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 727 506424 332669 783044 880396 711736 597152 162045 888697 203387 508244 201741 856316 195006 909328 053197 176660 188971 585497 553445 772847 715586 170300 > 4²²⁴ [i]