MinT - Best Known (167, 260, s)-Nets in Base 2

Best Known (167, 260, s)-Nets in Base 2

(167, 260, 112)-Net over F₂ — Constructive and digital

Digital (167, 260, 112)-net over F₂, using

t-expansion [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]

(167, 260, 149)-Net over F₂ — Digital

Digital (167, 260, 149)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 260, 825)-Net in Base 2 — Upper bound on s

There is no (167, 260, 826)-net in base 2, because

1 times m-reduction [i] would yield (167, 259, 826)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 955885 980273 077047 737246 560594 271272 187308 866284 361217 165506 977483 316715 111720 > 2²⁵⁹ [i]