MinT - Best Known (102, 102+24, s)-Nets in Base 8

Best Known (102, 102+24, s)-Nets in Base 8

Digital (102, 126, 21845)-net over F₈, using

net defined by OOA [i] based on linear OOA(8¹²⁶, 21845, F₈, 24, 24) (dual of [(21845, 24), 524154, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8¹²⁶, 262140, F₈, 24) (dual of [262140, 262014, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹²⁶, 262143, F₈, 24) (dual of [262143, 262017, 25]-code), using
    - 1 times truncation [i] based on linear OA(8¹²⁷, 262144, F₈, 25) (dual of [262144, 262017, 26]-code), using
      - an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]

Digital (102, 126, 174951)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8¹²⁶, 174951, F₈, 24) (dual of [174951, 174825, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹²⁶, 262143, F₈, 24) (dual of [262143, 262017, 25]-code), using
  - 1 times truncation [i] based on linear OA(8¹²⁷, 262144, F₈, 25) (dual of [262144, 262017, 26]-code), using
    - an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]

There is no (102, 126, large)-net in base 8, because

22 times m-reduction [i] would yield (102, 104, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]