MinT - Best Known (183−29, 183, s)-Nets in Base 2

Best Known (183−29, 183, s)-Nets in Base 2

Digital (154, 183, 585)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹⁸³, 585, F₂, 29, 29) (dual of [(585, 29), 16782, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2¹⁸³, 8191, F₂, 29) (dual of [8191, 8008, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁸³, 8192, F₂, 29) (dual of [8192, 8009, 30]-code), using
    - an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]

Digital (154, 183, 1689)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁸³, 1689, F₂, 4, 29) (dual of [(1689, 4), 6573, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁸³, 2048, F₂, 4, 29) (dual of [(2048, 4), 8009, 30]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹⁸³, 8192, F₂, 29) (dual of [8192, 8009, 30]-code), using
    - an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]

There is no (154, 183, 49508)-net in base 2, because

1 times m-reduction [i] would yield (154, 182, 49508)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 131456 213979 328084 603601 442923 849674 506758 316472 054392 > 2¹⁸² [i]