MinT - Best Known (113−15, 113, s)-Nets in Base 2

Best Known (113−15, 113, s)-Nets in Base 2

Digital (98, 113, 9362)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹¹³, 9362, F₂, 15, 15) (dual of [(9362, 15), 140317, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2¹¹³, 65535, F₂, 15) (dual of [65535, 65422, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹¹³, 65536, F₂, 15) (dual of [65536, 65423, 16]-code), using
    - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Digital (98, 113, 13107)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹¹³, 13107, F₂, 5, 15) (dual of [(13107, 5), 65422, 16]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2¹¹³, 65535, F₂, 15) (dual of [65535, 65422, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹¹³, 65536, F₂, 15) (dual of [65536, 65423, 16]-code), using
    - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

There is no (98, 113, 221503)-net in base 2, because

1 times m-reduction [i] would yield (98, 112, 221503)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5192 350403 717739 407978 152593 768346 > 2¹¹² [i]