MinT - Best Known (246−87, 246, s)-Nets in Base 2

Best Known (246−87, 246, s)-Nets in Base 2

(246−87, 246, 112)-Net over F₂ — Constructive and digital

Digital (159, 246, 112)-net over F₂, using

6 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]

(246−87, 246, 146)-Net over F₂ — Digital

Digital (159, 246, 146)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−87, 246, 814)-Net in Base 2 — Upper bound on s

There is no (159, 246, 815)-net in base 2, because

1 times m-reduction [i] would yield (159, 245, 815)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 58 426445 537018 509802 916766 586011 574950 691557 788529 306285 495926 655776 578562 > 2²⁴⁵ [i]