MinT - Best Known (247−90, 247, s)-Nets in Base 2

Best Known (247−90, 247, s)-Nets in Base 2

(247−90, 247, 112)-Net over F₂ — Constructive and digital

Digital (157, 247, 112)-net over F₂, using

1 times m-reduction [i] based on digital (157, 248, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 124, 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]

(247−90, 247, 137)-Net over F₂ — Digital

Digital (157, 247, 137)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−90, 247, 727)-Net in Base 2 — Upper bound on s

There is no (157, 247, 728)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 238 588920 120354 172355 063137 161663 395981 663130 213084 451590 249622 294897 679116 > 2²⁴⁷ [i]