MinT - Best Known (242−51, 242, s)-Nets in Base 2

Best Known (242−51, 242, s)-Nets in Base 2

(242−51, 242, 260)-Net over F₂ — Constructive and digital

Digital (191, 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]

(242−51, 242, 521)-Net over F₂ — Digital

Digital (191, 242, 521)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−51, 242, 8083)-Net in Base 2 — Upper bound on s

There is no (191, 242, 8084)-net in base 2, because

1 times m-reduction [i] would yield (191, 241, 8084)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 543964 010796 621844 016132 266157 829851 478572 652162 376516 720860 078309 356400 > 2²⁴¹ [i]