MinT - Best Known (158, 158+89, s)-Nets in Base 2

Best Known (158, 158+89, s)-Nets in Base 2

(158, 158+89, 112)-Net over F₂ — Constructive and digital

Digital (158, 247, 112)-net over F₂, using

3 times m-reduction [i] based on digital (158, 250, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 125, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(158, 158+89, 140)-Net over F₂ — Digital

Digital (158, 247, 140)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+89, 768)-Net in Base 2 — Upper bound on s

There is no (158, 247, 769)-net in base 2, because

1 times m-reduction [i] would yield (158, 246, 769)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 116 478528 773214 030546 987298 440546 704372 185492 467649 251650 395068 657333 008832 > 2²⁴⁶ [i]