MinT - Best Known (242−49, 242, s)-Nets in Base 2

Best Known (242−49, 242, s)-Nets in Base 2

(242−49, 242, 260)-Net over F₂ — Constructive and digital

Digital (193, 242, 260)-net over F₂, using

t-expansion [i] based on digital (192, 242, 260)-net over F₂, using
- 6 times m-reduction [i] based on digital (192, 248, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 62, 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]

(242−49, 242, 586)-Net over F₂ — Digital

Digital (193, 242, 586)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−49, 242, 10297)-Net in Base 2 — Upper bound on s

There is no (193, 242, 10298)-net in base 2, because

1 times m-reduction [i] would yield (193, 241, 10298)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 541415 428353 609802 166503 055896 948033 905578 347261 841171 344314 332677 871939 > 2²⁴¹ [i]