MinT - Best Known (259−78, 259, s)-Nets in Base 2

Best Known (259−78, 259, s)-Nets in Base 2

(259−78, 259, 132)-Net over F₂ — Constructive and digital

Digital (181, 259, 132)-net over F₂, using

t-expansion [i] based on digital (179, 259, 132)-net over F₂, using
- 1 times m-reduction [i] based on digital (179, 260, 132)-net over F₂, using
  - trace code for nets [i] based on digital (49, 130, 66)-net over F₄, using
    - net from sequence [i] based on digital (49, 65)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
        T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(259−78, 259, 220)-Net over F₂ — Digital

Digital (181, 259, 220)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−78, 259, 1479)-Net in Base 2 — Upper bound on s

There is no (181, 259, 1480)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 935152 507916 704244 965292 895026 227612 074056 214955 536569 978394 694930 242301 153494 > 2²⁵⁹ [i]