Best Known (92, 102, s)-Nets in Base 2
(92, 102, 209719)-Net over F2 — Constructive and digital
Digital (92, 102, 209719)-net over F2, using
- t-expansion [i] based on digital (91, 102, 209719)-net over F2, using
- net defined by OOA [i] based on linear OOA(2102, 209719, F2, 11, 11) (dual of [(209719, 11), 2306807, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2102, 1048596, F2, 11) (dual of [1048596, 1048494, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2102, 1048597, F2, 11) (dual of [1048597, 1048495, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(2101, 1048576, F2, 11) (dual of [1048576, 1048475, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(281, 1048576, F2, 9) (dual of [1048576, 1048495, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(21, 21, F2, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(2102, 1048597, F2, 11) (dual of [1048597, 1048495, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2102, 1048596, F2, 11) (dual of [1048596, 1048494, 12]-code), using
- net defined by OOA [i] based on linear OOA(2102, 209719, F2, 11, 11) (dual of [(209719, 11), 2306807, 12]-NRT-code), using
(92, 102, 277463)-Net over F2 — Digital
Digital (92, 102, 277463)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2102, 277463, F2, 3, 10) (dual of [(277463, 3), 832287, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2102, 349532, F2, 3, 10) (dual of [(349532, 3), 1048494, 11]-NRT-code), using
- strength reduction [i] based on linear OOA(2102, 349532, F2, 3, 11) (dual of [(349532, 3), 1048494, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2102, 1048596, F2, 11) (dual of [1048596, 1048494, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2102, 1048597, F2, 11) (dual of [1048597, 1048495, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(2101, 1048576, F2, 11) (dual of [1048576, 1048475, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(281, 1048576, F2, 9) (dual of [1048576, 1048495, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(21, 21, F2, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(2102, 1048597, F2, 11) (dual of [1048597, 1048495, 12]-code), using
- OOA 3-folding [i] based on linear OA(2102, 1048596, F2, 11) (dual of [1048596, 1048494, 12]-code), using
- strength reduction [i] based on linear OOA(2102, 349532, F2, 3, 11) (dual of [(349532, 3), 1048494, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2102, 349532, F2, 3, 10) (dual of [(349532, 3), 1048494, 11]-NRT-code), using
(92, 102, 3604518)-Net in Base 2 — Upper bound on s
There is no (92, 102, 3604519)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 5 070602 502973 004045 745228 413420 > 2102 [i]