MinT - Best Known (224−112, 224, s)-Nets in Base 4

Best Known (224−112, 224, s)-Nets in Base 4

(224−112, 224, 130)-Net over F₄ — Constructive and digital

Digital (112, 224, 130)-net over F₄, using

t-expansion [i] based on digital (105, 224, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(224−112, 224, 165)-Net over F₄ — Digital

Digital (112, 224, 165)-net over F₄, using

t-expansion [i] based on digital (109, 224, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(224−112, 224, 1806)-Net in Base 4 — Upper bound on s

There is no (112, 224, 1807)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 731 871593 504731 550252 587834 224927 891479 184279 553318 018952 524982 458115 650745 832940 574699 640137 996888 145842 440359 005706 121593 337816 514032 > 4²²⁴ [i]