MinT - Best Known (223−73, 223, s)-Nets in Base 2

Best Known (223−73, 223, s)-Nets in Base 2

(223−73, 223, 112)-Net over F₂ — Constructive and digital

Digital (150, 223, 112)-net over F₂, using

11 times m-reduction [i] based on digital (150, 234, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 117, 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]

(223−73, 223, 160)-Net over F₂ — Digital

Digital (150, 223, 160)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−73, 223, 973)-Net in Base 2 — Upper bound on s

There is no (150, 223, 974)-net in base 2, because

1 times m-reduction [i] would yield (150, 222, 974)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 834479 454456 487237 852816 944605 238218 697504 790244 171824 808695 462150 > 2²²² [i]