MinT - Best Known (230−71, 230, s)-Nets in Base 2

Best Known (230−71, 230, s)-Nets in Base 2

(230−71, 230, 112)-Net over F₂ — Constructive and digital

Digital (159, 230, 112)-net over F₂, using

22 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]

(230−71, 230, 188)-Net over F₂ — Digital

Digital (159, 230, 188)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−71, 230, 1245)-Net in Base 2 — Upper bound on s

There is no (159, 230, 1246)-net in base 2, because

1 times m-reduction [i] would yield (159, 229, 1246)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 869 833179 536484 276410 464354 994674 534621 397641 486584 699389 063193 048036 > 2²²⁹ [i]