MinT - Best Known (103−13, 103, s)-Nets in Base 2

Best Known (103−13, 103, s)-Nets in Base 2

Digital (90, 103, 21845)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹⁰³, 21845, F₂, 13, 13) (dual of [(21845, 13), 283882, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2¹⁰³, 131071, F₂, 13) (dual of [131071, 130968, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁰³, 131072, F₂, 13) (dual of [131072, 130969, 14]-code), using
    - an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Digital (90, 103, 26214)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁰³, 26214, F₂, 5, 13) (dual of [(26214, 5), 130967, 14]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2¹⁰³, 131070, F₂, 13) (dual of [131070, 130967, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁰³, 131072, F₂, 13) (dual of [131072, 130969, 14]-code), using
    - an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

There is no (90, 103, 392395)-net in base 2, because

1 times m-reduction [i] would yield (90, 102, 392395)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 070662 874650 160947 855090 077370 > 2¹⁰² [i]