MinT - Best Known (235−69, 235, s)-Nets in Base 2

Best Known (235−69, 235, s)-Nets in Base 2

(235−69, 235, 135)-Net over F₂ — Constructive and digital

Digital (166, 235, 135)-net over F₂, using

2¹ times duplication [i] based on digital (165, 234, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 78, 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]

(235−69, 235, 215)-Net over F₂ — Digital

Digital (166, 235, 215)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−69, 235, 1547)-Net in Base 2 — Upper bound on s

There is no (166, 235, 1548)-net in base 2, because

1 times m-reduction [i] would yield (166, 234, 1548)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28146 513602 603486 159552 624348 773108 824308 319807 437310 697730 037281 196272 > 2²³⁴ [i]