MinT - Best Known (218−73, 218, s)-Nets in Base 2

Best Known (218−73, 218, s)-Nets in Base 2

(218−73, 218, 112)-Net over F₂ — Constructive and digital

Digital (145, 218, 112)-net over F₂, using

6 times m-reduction [i] based on digital (145, 224, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 112, 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]

(218−73, 218, 149)-Net over F₂ — Digital

Digital (145, 218, 149)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−73, 218, 879)-Net in Base 2 — Upper bound on s

There is no (145, 218, 880)-net in base 2, because

1 times m-reduction [i] would yield (145, 217, 880)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 214158 591695 278324 309394 270357 693151 750205 180296 951616 670153 203863 > 2²¹⁷ [i]