MinT - Best Known (243−63, 243, s)-Nets in Base 2

Best Known (243−63, 243, s)-Nets in Base 2

(243−63, 243, 195)-Net over F₂ — Constructive and digital

Digital (180, 243, 195)-net over F₂, using

6 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]

(243−63, 243, 300)-Net over F₂ — Digital

Digital (180, 243, 300)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−63, 243, 2734)-Net in Base 2 — Upper bound on s

There is no (180, 243, 2735)-net in base 2, because

1 times m-reduction [i] would yield (180, 242, 2735)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 137343 920697 513412 590739 075607 643561 821991 580657 081117 001519 307797 534588 > 2²⁴² [i]