MinT - Best Known (16, 24, s)-Nets in Base 2

Best Known (16, 24, s)-Nets in Base 2

(16, 24, 39)-Net over F₂ — Constructive and digital

Digital (16, 24, 39)-net over F₂, using

2³ times duplication [i] based on digital (13, 21, 39)-net over F₂, using
- linear code embedding found in a computer search [i]

(16, 24, 40)-Net over F₂ — Digital

Digital (16, 24, 40)-net over F₂, using

2¹ times duplication [i] based on digital (15, 23, 40)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2²³, 40, F₂, 8, 8) (dual of [(40, 8), 297, 9]-NRT-code), using
  - appending kth column [i] based on linear OOA(2²³, 40, F₂, 7, 8) (dual of [(40, 7), 257, 9]-NRT-code), using
    - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²³, 40, F₂, 2, 8) (dual of [(40, 2), 57, 9]-NRT-code), using
      - 1 times NRT-code embedding in larger space [i] based on linear OOA(2²¹, 39, F₂, 2, 8) (dual of [(39, 2), 57, 9]-NRT-code), using
        extracting embedded OOA [i] based on digital (13, 21, 39)-net over F₂, using
        linear code embedding found in a computer search [i]

(16, 24, 136)-Net in Base 2 — Upper bound on s

There is no (16, 24, 137)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 17 138838 > 2²⁴ [i]