MinT - Best Known (170−37, 170, s)-Nets in Base 2

Best Known (170−37, 170, s)-Nets in Base 2

(170−37, 170, 196)-Net over F₂ — Constructive and digital

Digital (133, 170, 196)-net over F₂, using

2² times duplication [i] based on digital (131, 168, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 42, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(170−37, 170, 355)-Net over F₂ — Digital

Digital (133, 170, 355)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−37, 170, 5037)-Net in Base 2 — Upper bound on s

There is no (133, 170, 5038)-net in base 2, because

1 times m-reduction [i] would yield (133, 169, 5038)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 750 274637 471039 320505 748690 948281 730096 694128 852764 > 2¹⁶⁹ [i]