MinT - Best Known (253−91, 253, s)-Nets in Base 2

Best Known (253−91, 253, s)-Nets in Base 2

(253−91, 253, 112)-Net over F₂ — Constructive and digital

Digital (162, 253, 112)-net over F₂, using

5 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]

(253−91, 253, 144)-Net over F₂ — Digital

Digital (162, 253, 144)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−91, 253, 790)-Net in Base 2 — Upper bound on s

There is no (162, 253, 791)-net in base 2, because

1 times m-reduction [i] would yield (162, 252, 791)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7525 726420 984755 940269 927937 387059 347882 747390 983676 484965 438413 021860 905536 > 2²⁵² [i]