MinT - Best Known (163, 163+60, s)-Nets in Base 2

Best Known (163, 163+60, s)-Nets in Base 2

(163, 163+60, 195)-Net over F₂ — Constructive and digital

Digital (163, 223, 195)-net over F₂, using

2¹ times duplication [i] based on digital (162, 222, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 74, 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]

(163, 163+60, 254)-Net over F₂ — Digital

Digital (163, 223, 254)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+60, 2037)-Net in Base 2 — Upper bound on s

There is no (163, 223, 2038)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13 526878 034747 755237 033596 445565 550152 104773 776049 588304 182545 532432 > 2²²³ [i]