MinT - Best Known (257−95, 257, s)-Nets in Base 2

Best Known (257−95, 257, s)-Nets in Base 2

(257−95, 257, 112)-Net over F₂ — Constructive and digital

Digital (162, 257, 112)-net over F₂, using

1 times m-reduction [i] based on digital (162, 258, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 129, 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]

(257−95, 257, 137)-Net over F₂ — Digital

Digital (162, 257, 137)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−95, 257, 733)-Net in Base 2 — Upper bound on s

There is no (162, 257, 734)-net in base 2, because

1 times m-reduction [i] would yield (162, 256, 734)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 116513 070425 387638 318244 732279 020647 845664 018456 672170 074719 194034 729160 003912 > 2²⁵⁶ [i]