MinT - Best Known (220−58, 220, s)-Nets in Base 2

Best Known (220−58, 220, s)-Nets in Base 2

(220−58, 220, 195)-Net over F₂ — Constructive and digital

Digital (162, 220, 195)-net over F₂, using

2 times m-reduction [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]

(220−58, 220, 264)-Net over F₂ — Digital

Digital (162, 220, 264)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−58, 220, 2200)-Net in Base 2 — Upper bound on s

There is no (162, 220, 2201)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 702271 790979 241031 318738 413381 802956 169345 938213 037144 232475 449120 > 2²²⁰ [i]