MinT - Best Known (242−52, 242, s)-Nets in Base 2

Best Known (242−52, 242, s)-Nets in Base 2

(242−52, 242, 260)-Net over F₂ — Constructive and digital

Digital (190, 242, 260)-net over F₂, using

t-expansion [i] based on digital (189, 242, 260)-net over F₂, using
- 2 times m-reduction [i] based on digital (189, 244, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 61, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(242−52, 242, 493)-Net over F₂ — Digital

Digital (190, 242, 493)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−52, 242, 6647)-Net in Base 2 — Upper bound on s

There is no (190, 242, 6648)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 069364 297949 398924 359679 101716 797977 624298 329344 767316 230449 051890 807308 > 2²⁴² [i]