MinT - Best Known (230−74, 230, s)-Nets in Base 2

Best Known (230−74, 230, s)-Nets in Base 2

(230−74, 230, 112)-Net over F₂ — Constructive and digital

Digital (156, 230, 112)-net over F₂, using

16 times m-reduction [i] based on digital (156, 246, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 123, 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]

(230−74, 230, 171)-Net over F₂ — Digital

Digital (156, 230, 171)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−74, 230, 1035)-Net in Base 2 — Upper bound on s

There is no (156, 230, 1036)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1748 017299 515658 102459 565347 270659 482436 346956 761424 439878 956371 953856 > 2²³⁰ [i]