MinT - Best Known (204−69, 204, s)-Nets in Base 2

Best Known (204−69, 204, s)-Nets in Base 2

(204−69, 204, 112)-Net over F₂ — Constructive and digital

Digital (135, 204, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 102, 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]

(204−69, 204, 138)-Net over F₂ — Digital

Digital (135, 204, 138)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−69, 204, 799)-Net in Base 2 — Upper bound on s

There is no (135, 204, 800)-net in base 2, because

1 times m-reduction [i] would yield (135, 203, 800)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13 050770 769238 934901 176913 452856 052404 093994 417417 164528 941208 > 2²⁰³ [i]