MinT - Best Known (147, 147+69, s)-Nets in Base 2

Best Known (147, 147+69, s)-Nets in Base 2

(147, 147+69, 112)-Net over F₂ — Constructive and digital

Digital (147, 216, 112)-net over F₂, using

12 times m-reduction [i] based on digital (147, 228, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 114, 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]

(147, 147+69, 164)-Net over F₂ — Digital

Digital (147, 216, 164)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+69, 1034)-Net in Base 2 — Upper bound on s

There is no (147, 216, 1035)-net in base 2, because

1 times m-reduction [i] would yield (147, 215, 1035)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 53328 782034 719249 360660 752369 371570 101528 095622 493843 462875 930464 > 2²¹⁵ [i]