MinT - Best Known (241−61, 241, s)-Nets in Base 2

Best Known (241−61, 241, s)-Nets in Base 2

(241−61, 241, 195)-Net over F₂ — Constructive and digital

Digital (180, 241, 195)-net over F₂, using

8 times m-reduction [i] based on digital (180, 249, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 83, 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]

(241−61, 241, 317)-Net over F₂ — Digital

Digital (180, 241, 317)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−61, 241, 3039)-Net in Base 2 — Upper bound on s

There is no (180, 241, 3040)-net in base 2, because

1 times m-reduction [i] would yield (180, 240, 3040)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 780946 851522 699433 320230 605748 037147 392380 231280 867706 235332 245248 174787 > 2²⁴⁰ [i]