MinT - Best Known (224−146, 224, s)-Nets in Base 4

Best Known (224−146, 224, s)-Nets in Base 4

(224−146, 224, 104)-Net over F₄ — Constructive and digital

Digital (78, 224, 104)-net over F₄, using

t-expansion [i] based on digital (73, 224, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(224−146, 224, 112)-Net over F₄ — Digital

Digital (78, 224, 112)-net over F₄, using

t-expansion [i] based on digital (73, 224, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(224−146, 224, 598)-Net in Base 4 — Upper bound on s

There is no (78, 224, 599)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 753 500910 123002 002388 284809 275006 585529 613774 082977 669730 151047 968091 978038 600412 018761 521220 439392 522249 040716 289316 326211 820953 405340 > 4²²⁴ [i]