MinT - Best Known (225−64, 225, s)-Nets in Base 4

Best Known (225−64, 225, s)-Nets in Base 4

(225−64, 225, 531)-Net over F₄ — Constructive and digital

Digital (161, 225, 531)-net over F₄, using

6 times m-reduction [i] based on digital (161, 231, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 77, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(225−64, 225, 1149)-Net over F₄ — Digital

Digital (161, 225, 1149)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−64, 225, 72918)-Net in Base 4 — Upper bound on s

There is no (161, 225, 72919)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2908 013284 294907 335831 005253 417001 058910 549145 056181 252307 072155 887516 671676 977173 680244 247713 660992 126013 166399 337064 106913 886208 363190 > 4²²⁵ [i]