MinT - Best Known (252−71, 252, s)-Nets in Base 2

Best Known (252−71, 252, s)-Nets in Base 2

(252−71, 252, 144)-Net over F₂ — Constructive and digital

Digital (181, 252, 144)-net over F₂, using

3 times m-reduction [i] based on digital (181, 255, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 85, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(252−71, 252, 253)-Net over F₂ — Digital

Digital (181, 252, 253)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−71, 252, 1953)-Net in Base 2 — Upper bound on s

There is no (181, 252, 1954)-net in base 2, because

1 times m-reduction [i] would yield (181, 251, 1954)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3653 693375 320014 434613 994551 072668 590801 180146 257744 830706 544846 634550 213540 > 2²⁵¹ [i]