MinT - Best Known (111, 111+43, s)-Nets in Base 2

Best Known (111, 111+43, s)-Nets in Base 2

(111, 111+43, 112)-Net over F₂ — Constructive and digital

Digital (111, 154, 112)-net over F₂, using

2 times m-reduction [i] based on digital (111, 156, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 78, 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, 111+43, 171)-Net over F₂ — Digital

Digital (111, 154, 171)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+43, 1323)-Net in Base 2 — Upper bound on s

There is no (111, 154, 1324)-net in base 2, because

1 times m-reduction [i] would yield (111, 153, 1324)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11487 665868 929363 145784 592736 897791 675036 871980 > 2¹⁵³ [i]