MinT - Best Known (238−82, 238, s)-Nets in Base 2

Best Known (238−82, 238, s)-Nets in Base 2

(238−82, 238, 112)-Net over F₂ — Constructive and digital

Digital (156, 238, 112)-net over F₂, using

8 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]

(238−82, 238, 150)-Net over F₂ — Digital

Digital (156, 238, 150)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−82, 238, 843)-Net in Base 2 — Upper bound on s

There is no (156, 238, 844)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 459535 709007 204802 823979 946045 103943 816520 946355 200246 693405 683315 226550 > 2²³⁸ [i]