MinT - Best Known (22, 28, s)-Nets in Base 2

Best Known (22, 28, s)-Nets in Base 2

(22, 28, 510)-Net over F₂ — Constructive and digital

Digital (22, 28, 510)-net over F₂, using

1 times m-reduction [i] based on digital (22, 29, 510)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2²⁹, 510, F₂, 7, 7) (dual of [(510, 7), 3541, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2²⁹, 511, F₂, 3, 7) (dual of [(511, 3), 1504, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(22, 28, 511)-Net over F₂ — Digital

Digital (22, 28, 511)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²⁸, 511, F₂, 6, 6) (dual of [(511, 6), 3038, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2²⁸, 511, F₂, 5, 6) (dual of [(511, 5), 2527, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁸, 511, F₂, 2, 6) (dual of [(511, 2), 994, 7]-NRT-code), using
    - OOAs constructed from BCH codes [i]

(22, 28, 1168)-Net in Base 2 — Upper bound on s

There is no (22, 28, 1169)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 268 990408 > 2²⁸ [i]