MinT - Best Known (229−71, 229, s)-Nets in Base 2

Best Known (229−71, 229, s)-Nets in Base 2

(229−71, 229, 112)-Net over F₂ — Constructive and digital

Digital (158, 229, 112)-net over F₂, using

21 times m-reduction [i] based on digital (158, 250, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 125, 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]

(229−71, 229, 185)-Net over F₂ — Digital

Digital (158, 229, 185)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−71, 229, 1220)-Net in Base 2 — Upper bound on s

There is no (158, 229, 1221)-net in base 2, because

1 times m-reduction [i] would yield (158, 228, 1221)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 439 932863 451167 786686 067051 342205 938183 677046 202709 006084 228250 111680 > 2²²⁸ [i]