MinT - Best Known (242−59, 242, s)-Nets in Base 2

Best Known (242−59, 242, s)-Nets in Base 2

(242−59, 242, 195)-Net over F₂ — Constructive and digital

Digital (183, 242, 195)-net over F₂, using

t-expansion [i] based on digital (182, 242, 195)-net over F₂, using
- 10 times m-reduction [i] based on digital (182, 252, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 84, 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]

(242−59, 242, 351)-Net over F₂ — Digital

Digital (183, 242, 351)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−59, 242, 3662)-Net in Base 2 — Upper bound on s

There is no (183, 242, 3663)-net in base 2, because

1 times m-reduction [i] would yield (183, 241, 3663)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 555877 598949 210990 607138 158915 792740 133036 973740 156768 204493 346715 963632 > 2²⁴¹ [i]