MinT - Best Known (241−82, 241, s)-Nets in Base 2

Best Known (241−82, 241, s)-Nets in Base 2

(241−82, 241, 112)-Net over F₂ — Constructive and digital

Digital (159, 241, 112)-net over F₂, using

11 times m-reduction [i] based on digital (159, 252, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 126, 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]

(241−82, 241, 156)-Net over F₂ — Digital

Digital (159, 241, 156)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−82, 241, 889)-Net in Base 2 — Upper bound on s

There is no (159, 241, 890)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 535589 093067 411013 341581 999001 705674 337864 289282 985514 585431 222863 054541 > 2²⁴¹ [i]