MinT - Best Known (111−76, 111, s)-Nets in Base 4

Best Known (111−76, 111, s)-Nets in Base 4

(111−76, 111, 56)-Net over F₄ — Constructive and digital

Digital (35, 111, 56)-net over F₄, using

t-expansion [i] based on digital (33, 111, 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]

(111−76, 111, 65)-Net over F₄ — Digital

Digital (35, 111, 65)-net over F₄, using

t-expansion [i] based on digital (33, 111, 65)-net over F₄, using
- net from sequence [i] based on digital (33, 64)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 65, using
    - Drinfeld modules of rank 1 [i]

(111−76, 111, 257)-Net in Base 4 — Upper bound on s

There is no (35, 111, 258)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 338928 533773 641670 604325 534703 188812 193535 867640 474853 548216 641920 > 4¹¹¹ [i]