MinT - Best Known (160−47, 160, s)-Nets in Base 2

Best Known (160−47, 160, s)-Nets in Base 2

(160−47, 160, 112)-Net over F₂ — Constructive and digital

Digital (113, 160, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 80, 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]

(160−47, 160, 156)-Net over F₂ — Digital

Digital (113, 160, 156)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−47, 160, 1102)-Net in Base 2 — Upper bound on s

There is no (113, 160, 1103)-net in base 2, because

1 times m-reduction [i] would yield (113, 159, 1103)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 734487 402639 383678 516781 731201 698221 544537 068168 > 2¹⁵⁹ [i]