MinT - Best Known (84, 84+13, s)-Nets in Base 2

Best Known (84, 84+13, s)-Nets in Base 2

Digital (84, 97, 10922)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁹⁷, 10922, F₂, 13, 13) (dual of [(10922, 13), 141889, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2⁹⁷, 65533, F₂, 13) (dual of [65533, 65436, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁹⁷, 65536, F₂, 13) (dual of [65536, 65439, 14]-code), using
    - an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Digital (84, 97, 13107)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁹⁷, 13107, F₂, 5, 13) (dual of [(13107, 5), 65438, 14]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2⁹⁷, 65535, F₂, 13) (dual of [65535, 65438, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁹⁷, 65536, F₂, 13) (dual of [65536, 65439, 14]-code), using
    - an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

There is no (84, 97, 196193)-net in base 2, because

1 times m-reduction [i] would yield (84, 96, 196193)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 79228 501405 269736 098499 953040 > 2⁹⁶ [i]