MinT - Best Known (233−71, 233, s)-Nets in Base 2

Best Known (233−71, 233, s)-Nets in Base 2

(233−71, 233, 112)-Net over F₂ — Constructive and digital

Digital (162, 233, 112)-net over F₂, using

25 times m-reduction [i] based on digital (162, 258, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 129, 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]

(233−71, 233, 196)-Net over F₂ — Digital

Digital (162, 233, 196)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−71, 233, 1325)-Net in Base 2 — Upper bound on s

There is no (162, 233, 1326)-net in base 2, because

1 times m-reduction [i] would yield (162, 232, 1326)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7075 652075 770297 801101 585784 582493 611947 101615 803001 268894 619419 118590 > 2²³² [i]