MinT - Best Known (242−61, 242, s)-Nets in Base 2

Best Known (242−61, 242, s)-Nets in Base 2

(242−61, 242, 195)-Net over F₂ — Constructive and digital

Digital (181, 242, 195)-net over F₂, using

t-expansion [i] based on digital (180, 242, 195)-net over F₂, using
- 7 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]

(242−61, 242, 321)-Net over F₂ — Digital

Digital (181, 242, 321)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−61, 242, 3111)-Net in Base 2 — Upper bound on s

There is no (181, 242, 3112)-net in base 2, because

1 times m-reduction [i] would yield (181, 241, 3112)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 559072 888004 389314 280586 074301 396822 684832 708249 635695 457936 984868 886524 > 2²⁴¹ [i]