MinT - Best Known (187, 242, s)-Nets in Base 2

Best Known (187, 242, s)-Nets in Base 2

(187, 242, 206)-Net over F₂ — Constructive and digital

Digital (187, 242, 206)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (8, 35, 11)-net over F₂, using
  - net from sequence [i] based on digital (8, 10)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 8 and N(F) ≥ 11, using
      - an explicitly constructive algebraic function field [i]
2. digital (152, 207, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 69, 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]

(187, 242, 423)-Net over F₂ — Digital

Digital (187, 242, 423)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(187, 242, 5273)-Net in Base 2 — Upper bound on s

There is no (187, 242, 5274)-net in base 2, because

1 times m-reduction [i] would yield (187, 241, 5274)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 540758 548420 332499 596852 094846 175692 482249 369020 109119 944565 199716 358788 > 2²⁴¹ [i]