MinT - Best Known (194−41, 194, s)-Nets in Base 2

Best Known (194−41, 194, s)-Nets in Base 2

(194−41, 194, 260)-Net over F₂ — Constructive and digital

Digital (153, 194, 260)-net over F₂, using

2 times m-reduction [i] based on digital (153, 196, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 49, 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]

(194−41, 194, 430)-Net over F₂ — Digital

Digital (153, 194, 430)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−41, 194, 6642)-Net in Base 2 — Upper bound on s

There is no (153, 194, 6643)-net in base 2, because

1 times m-reduction [i] would yield (153, 193, 6643)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12576 791247 837551 340459 109340 258754 815665 204845 093354 656512 > 2¹⁹³ [i]