MinT - Best Known (253−71, 253, s)-Nets in Base 2

Best Known (253−71, 253, s)-Nets in Base 2

(253−71, 253, 144)-Net over F₂ — Constructive and digital

Digital (182, 253, 144)-net over F₂, using

t-expansion [i] based on digital (181, 253, 144)-net over F₂, using
- 2 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]

(253−71, 253, 256)-Net over F₂ — Digital

Digital (182, 253, 256)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−71, 253, 1993)-Net in Base 2 — Upper bound on s

There is no (182, 253, 1994)-net in base 2, because

1 times m-reduction [i] would yield (182, 252, 1994)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7294 981086 974301 375636 041959 210186 167354 095573 130656 358800 118091 908669 897504 > 2²⁵² [i]