MinT - Best Known (194−80, 194, s)-Nets in Base 2

Best Known (194−80, 194, s)-Nets in Base 2

(194−80, 194, 66)-Net over F₂ — Constructive and digital

Digital (114, 194, 66)-net over F₂, using

4 times m-reduction [i] based on digital (114, 198, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 99, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(194−80, 194, 84)-Net over F₂ — Digital

Digital (114, 194, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−80, 194, 398)-Net in Base 2 — Upper bound on s

There is no (114, 194, 399)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26041 210433 894381 072324 430645 215126 964403 207451 259200 150252 > 2¹⁹⁴ [i]