MinT - Best Known (236−78, 236, s)-Nets in Base 2

Best Known (236−78, 236, s)-Nets in Base 2

(236−78, 236, 112)-Net over F₂ — Constructive and digital

Digital (158, 236, 112)-net over F₂, using

14 times m-reduction [i] based on digital (158, 250, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 125, 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]

(236−78, 236, 164)-Net over F₂ — Digital

Digital (158, 236, 164)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−78, 236, 964)-Net in Base 2 — Upper bound on s

There is no (158, 236, 965)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 112544 364462 559833 269794 902303 476487 397050 139269 022733 431127 811746 219120 > 2²³⁶ [i]