MinT - Best Known (254−23, 254, s)-Nets in Base 2

Best Known (254−23, 254, s)-Nets in Base 2

Digital (231, 254, 762600)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²⁵⁴, 762600, F₂, 23, 23) (dual of [(762600, 23), 17539546, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2²⁵⁴, 8388601, F₂, 23) (dual of [8388601, 8388347, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁵⁴, large, F₂, 23) (dual of [large, large−254, 24]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

Digital (231, 254, 1048575)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁵⁴, 1048575, F₂, 8, 23) (dual of [(1048575, 8), 8388346, 24]-NRT-code), using
- OOA 8-folding [i] based on linear OA(2²⁵⁴, 8388600, F₂, 23) (dual of [8388600, 8388346, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁵⁴, large, F₂, 23) (dual of [large, large−254, 24]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

There is no (231, 254, large)-net in base 2, because

21 times m-reduction [i] would yield (231, 233, large)-net in base 2, but
- mutually orthogonal hypercube bound [i]