MinT - Best Known (254−72, 254, s)-Nets in Base 2

Best Known (254−72, 254, s)-Nets in Base 2

(254−72, 254, 144)-Net over F₂ — Constructive and digital

Digital (182, 254, 144)-net over F₂, using

t-expansion [i] based on digital (181, 254, 144)-net over F₂, using
- 1 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]

(254−72, 254, 251)-Net over F₂ — Digital

Digital (182, 254, 251)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−72, 254, 1846)-Net in Base 2 — Upper bound on s

There is no (182, 254, 1847)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 29047 753812 403662 022803 568766 523612 723830 826860 880865 652461 754055 201664 272765 > 2²⁵⁴ [i]