MinT - Best Known (220−69, 220, s)-Nets in Base 2

Best Known (220−69, 220, s)-Nets in Base 2

(220−69, 220, 112)-Net over F₂ — Constructive and digital

Digital (151, 220, 112)-net over F₂, using

16 times m-reduction [i] based on digital (151, 236, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 118, 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]

(220−69, 220, 174)-Net over F₂ — Digital

Digital (151, 220, 174)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−69, 220, 1126)-Net in Base 2 — Upper bound on s

There is no (151, 220, 1127)-net in base 2, because

1 times m-reduction [i] would yield (151, 219, 1127)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 851807 418929 305718 010032 463553 239863 643011 957373 479057 467796 002557 > 2²¹⁹ [i]