MinT - Best Known (244−70, 244, s)-Nets in Base 2

Best Known (244−70, 244, s)-Nets in Base 2

(244−70, 244, 144)-Net over F₂ — Constructive and digital

Digital (174, 244, 144)-net over F₂, using

2¹ times duplication [i] based on digital (173, 243, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 81, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(244−70, 244, 235)-Net over F₂ — Digital

Digital (174, 244, 235)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−70, 244, 1694)-Net in Base 2 — Upper bound on s

There is no (174, 244, 1695)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28 836555 940262 590159 569262 804333 810463 802994 613702 622625 867856 990018 341336 > 2²⁴⁴ [i]