MinT - Best Known (242−71, 242, s)-Nets in Base 2

Best Known (242−71, 242, s)-Nets in Base 2

(242−71, 242, 135)-Net over F₂ — Constructive and digital

Digital (171, 242, 135)-net over F₂, using

1 times m-reduction [i] based on digital (171, 243, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 81, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(242−71, 242, 221)-Net over F₂ — Digital

Digital (171, 242, 221)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−71, 242, 1593)-Net in Base 2 — Upper bound on s

There is no (171, 242, 1594)-net in base 2, because

1 times m-reduction [i] would yield (171, 241, 1594)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 580750 714319 651545 083779 321920 377243 372886 749944 539854 564607 201713 729640 > 2²⁴¹ [i]