MinT - Best Known (259−96, 259, s)-Nets in Base 2

Best Known (259−96, 259, s)-Nets in Base 2

(259−96, 259, 112)-Net over F₂ — Constructive and digital

Digital (163, 259, 112)-net over F₂, using

1 times m-reduction [i] based on digital (163, 260, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 130, 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]

(259−96, 259, 137)-Net over F₂ — Digital

Digital (163, 259, 137)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−96, 259, 720)-Net in Base 2 — Upper bound on s

There is no (163, 259, 721)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 962914 008260 184675 264041 046191 917115 530716 197619 798291 449440 673503 955445 249830 > 2²⁵⁹ [i]