MinT - Best Known (189, 189+53, s)-Nets in Base 2

Best Known (189, 189+53, s)-Nets in Base 2

(189, 189+53, 260)-Net over F₂ — Constructive and digital

Digital (189, 242, 260)-net over F₂, using

2 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+53, 467)-Net over F₂ — Digital

Digital (189, 242, 467)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(189, 189+53, 6472)-Net in Base 2 — Upper bound on s

There is no (189, 242, 6473)-net in base 2, because

1 times m-reduction [i] would yield (189, 241, 6473)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 547383 777338 612126 518774 867706 121752 998756 250310 871710 707302 120950 382640 > 2²⁴¹ [i]