MinT - Best Known (223−61, 223, s)-Nets in Base 4

Best Known (223−61, 223, s)-Nets in Base 4

(223−61, 223, 531)-Net over F₄ — Constructive and digital

Digital (162, 223, 531)-net over F₄, using

t-expansion [i] based on digital (161, 223, 531)-net over F₄, using
- 8 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]

(223−61, 223, 1358)-Net over F₄ — Digital

Digital (162, 223, 1358)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−61, 223, 114503)-Net in Base 4 — Upper bound on s

There is no (162, 223, 114504)-net in base 4, because

1 times m-reduction [i] would yield (162, 222, 114504)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 434370 915099 443669 322375 272310 478111 782178 662769 266168 182198 116373 771655 606528 246842 754818 212622 190500 208482 845774 280102 365794 936616 > 4²²² [i]