MinT - Best Known (143−102, 143, s)-Nets in Base 4

Best Known (143−102, 143, s)-Nets in Base 4

(143−102, 143, 56)-Net over F₄ — Constructive and digital

Digital (41, 143, 56)-net over F₄, using

t-expansion [i] based on digital (33, 143, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(143−102, 143, 75)-Net over F₄ — Digital

Digital (41, 143, 75)-net over F₄, using

t-expansion [i] based on digital (40, 143, 75)-net over F₄, using
- net from sequence [i] based on digital (40, 74)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 40 and N(F) ≥ 75, using
    - Drinfeld modules of rank 1 [i]

(143−102, 143, 282)-Net in Base 4 — Upper bound on s

There is no (41, 143, 283)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 130 245063 807847 139600 303175 379583 171293 885475 516004 226007 910397 609392 114403 212660 738400 > 4¹⁴³ [i]