MinT - Best Known (207−61, 207, s)-Nets in Base 2

Best Known (207−61, 207, s)-Nets in Base 2

(207−61, 207, 112)-Net over F₂ — Constructive and digital

Digital (146, 207, 112)-net over F₂, using

19 times m-reduction [i] based on digital (146, 226, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 113, 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]

(207−61, 207, 192)-Net over F₂ — Digital

Digital (146, 207, 192)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−61, 207, 1361)-Net in Base 2 — Upper bound on s

There is no (146, 207, 1362)-net in base 2, because

1 times m-reduction [i] would yield (146, 206, 1362)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 103 433704 847488 703056 091686 168095 620678 390972 926475 637668 637344 > 2²⁰⁶ [i]