MinT - Best Known (28−3, 28, s)-Nets in Base 2

Best Known (28−3, 28, s)-Nets in Base 2

(28−3, 28, large)-Net over F₂ — Constructive and digital

Digital (25, 28, large)-net over F₂, using

2⁴ times duplication [i] based on digital (21, 24, large)-net over F₂, using
- net defined by OOA [i] based on linear OOA(2²⁴, large, F₂, 3, 3), using
  - OOA stacking with additional row [i] based on linear OA(2²⁴, large, F₂, 3) (dual of [large, large−24, 4]-code), using
    - caps in base bÂ =Â 2 [i]

(28−3, 28, large)-Net in Base 2 — Upper bound on s

There is no (25, 28, large)-net in base 2, because

1 times m-reduction [i] would yield (25, 27, large)-net in base 2, but
- mutually orthogonal hypercube bound [i]