MinT - Best Known (150, 197, s)-Nets in Base 2

Best Known (150, 197, s)-Nets in Base 2

(150, 197, 195)-Net over F₂ — Constructive and digital

Digital (150, 197, 195)-net over F₂, using

7 times m-reduction [i] based on digital (150, 204, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 68, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(150, 197, 313)-Net over F₂ — Digital

Digital (150, 197, 313)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 197, 3431)-Net in Base 2 — Upper bound on s

There is no (150, 197, 3432)-net in base 2, because

1 times m-reduction [i] would yield (150, 196, 3432)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 100722 358311 328159 393880 869646 167505 885087 919113 372852 235590 > 2¹⁹⁶ [i]