MinT - Best Known (197−65, 197, s)-Nets in Base 2

Best Known (197−65, 197, s)-Nets in Base 2

(197−65, 197, 112)-Net over F₂ — Constructive and digital

Digital (132, 197, 112)-net over F₂, using

1 times m-reduction [i] based on digital (132, 198, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 99, 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]

(197−65, 197, 141)-Net over F₂ — Digital

Digital (132, 197, 141)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−65, 197, 846)-Net in Base 2 — Upper bound on s

There is no (132, 197, 847)-net in base 2, because

1 times m-reduction [i] would yield (132, 196, 847)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 103025 656099 885842 945385 918733 796765 897361 943245 089411 706950 > 2¹⁹⁶ [i]