MinT - Best Known (224−116, 224, s)-Nets in Base 4

Best Known (224−116, 224, s)-Nets in Base 4

(224−116, 224, 130)-Net over F₄ — Constructive and digital

Digital (108, 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]

(224−116, 224, 144)-Net over F₄ — Digital

Digital (108, 224, 144)-net over F₄, using

t-expansion [i] based on digital (91, 224, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(224−116, 224, 1535)-Net in Base 4 — Upper bound on s

There is no (108, 224, 1536)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 752 251846 054417 060906 546865 333593 562358 542949 220219 570027 197595 122768 477077 440407 581821 236447 938773 451485 398880 105756 685529 500710 071505 > 4²²⁴ [i]