MinT - Best Known (15, 15+9, s)-Nets in Base 2

Best Known (15, 15+9, s)-Nets in Base 2

(15, 15+9, 29)-Net over F₂ — Constructive and digital

Digital (15, 24, 29)-net over F₂, using

2³ times duplication [i] based on digital (12, 21, 29)-net over F₂, using
- linear code embedding found in a computer search [i]

(15, 15+9, 30)-Net over F₂ — Digital

Digital (15, 24, 30)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²⁴, 30, F₂, 9, 9) (dual of [(30, 9), 246, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2²⁴, 30, F₂, 8, 9) (dual of [(30, 8), 216, 10]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁴, 30, F₂, 2, 9) (dual of [(30, 2), 36, 10]-NRT-code), using
    - 2¹ times duplication [i] based on linear OOA(2²³, 30, F₂, 2, 9) (dual of [(30, 2), 37, 10]-NRT-code), using
      - 1 times NRT-code embedding in larger space [i] based on linear OOA(2²¹, 29, F₂, 2, 9) (dual of [(29, 2), 37, 10]-NRT-code), using
        extracting embedded OOA [i] based on digital (12, 21, 29)-net over F₂, using
        linear code embedding found in a computer search [i]

(15, 15+9, 113)-Net in Base 2 — Upper bound on s

There is no (15, 24, 114)-net in base 2, because

1 times m-reduction [i] would yield (15, 23, 114)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 8 467332 > 2²³ [i]