MinT - Best Known (247−73, 247, s)-Nets in Base 2

Best Known (247−73, 247, s)-Nets in Base 2

(247−73, 247, 135)-Net over F₂ — Constructive and digital

Digital (174, 247, 135)-net over F₂, using

2¹ times duplication [i] based on digital (173, 246, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 82, 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]

(247−73, 247, 221)-Net over F₂ — Digital

Digital (174, 247, 221)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−73, 247, 1575)-Net in Base 2 — Upper bound on s

There is no (174, 247, 1576)-net in base 2, because

1 times m-reduction [i] would yield (174, 246, 1576)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 113 718091 915301 220683 311834 690959 967989 691789 031554 045328 950750 991536 888035 > 2²⁴⁶ [i]