Best Known (198−29, 198, s)-Nets in Base 2
(198−29, 198, 1171)-Net over F2 — Constructive and digital
Digital (169, 198, 1171)-net over F2, using
- net defined by OOA [i] based on linear OOA(2198, 1171, F2, 29, 29) (dual of [(1171, 29), 33761, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2198, 16395, F2, 29) (dual of [16395, 16197, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2198, 16399, F2, 29) (dual of [16399, 16201, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2197, 16384, F2, 29) (dual of [16384, 16187, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(28) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(2198, 16399, F2, 29) (dual of [16399, 16201, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2198, 16395, F2, 29) (dual of [16395, 16197, 30]-code), using
(198−29, 198, 3133)-Net over F2 — Digital
Digital (169, 198, 3133)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2198, 3133, F2, 5, 29) (dual of [(3133, 5), 15467, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2198, 3279, F2, 5, 29) (dual of [(3279, 5), 16197, 30]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2198, 16395, F2, 29) (dual of [16395, 16197, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2198, 16399, F2, 29) (dual of [16399, 16201, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2197, 16384, F2, 29) (dual of [16384, 16187, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(28) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(2198, 16399, F2, 29) (dual of [16399, 16201, 30]-code), using
- OOA 5-folding [i] based on linear OA(2198, 16395, F2, 29) (dual of [16395, 16197, 30]-code), using
- discarding factors / shortening the dual code based on linear OOA(2198, 3279, F2, 5, 29) (dual of [(3279, 5), 16197, 30]-NRT-code), using
(198−29, 198, 104062)-Net in Base 2 — Upper bound on s
There is no (169, 198, 104063)-net in base 2, because
- 1 times m-reduction [i] would yield (169, 197, 104063)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 200880 587468 761259 079173 323415 733935 032475 151468 849081 657987 > 2197 [i]