MinT - Best Known (189, 189+49, s)-Nets in Base 2

Best Known (189, 189+49, s)-Nets in Base 2

(189, 189+49, 260)-Net over F₂ — Constructive and digital

Digital (189, 238, 260)-net over F₂, using

6 times m-reduction [i] based on digital (189, 244, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 61, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(189, 189+49, 549)-Net over F₂ — Digital

Digital (189, 238, 549)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(189, 189+49, 9169)-Net in Base 2 — Upper bound on s

There is no (189, 238, 9170)-net in base 2, because

1 times m-reduction [i] would yield (189, 237, 9170)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 220983 997115 501250 909760 652710 792220 088560 595517 712540 379834 696416 423192 > 2²³⁷ [i]