MinT - Best Known (113−72, 113, s)-Nets in Base 4

Best Known (113−72, 113, s)-Nets in Base 4

(113−72, 113, 56)-Net over F₄ — Constructive and digital

Digital (41, 113, 56)-net over F₄, using

t-expansion [i] based on digital (33, 113, 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]

(113−72, 113, 75)-Net over F₄ — Digital

Digital (41, 113, 75)-net over F₄, using

t-expansion [i] based on digital (40, 113, 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]

(113−72, 113, 340)-Net in Base 4 — Upper bound on s

There is no (41, 113, 341)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 111 059783 085145 082222 217780 768875 771173 627961 365013 272637 896424 101570 > 4¹¹³ [i]