Best Known (37, 49, s)-Nets in Base 16
(37, 49, 21847)-Net over F16 — Constructive and digital
Digital (37, 49, 21847)-net over F16, using
- 161 times duplication [i] based on digital (36, 48, 21847)-net over F16, using
- net defined by OOA [i] based on linear OOA(1648, 21847, F16, 12, 12) (dual of [(21847, 12), 262116, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(1648, 131082, F16, 12) (dual of [131082, 131034, 13]-code), using
- trace code [i] based on linear OA(25624, 65541, F256, 12) (dual of [65541, 65517, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- trace code [i] based on linear OA(25624, 65541, F256, 12) (dual of [65541, 65517, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(1648, 131082, F16, 12) (dual of [131082, 131034, 13]-code), using
- net defined by OOA [i] based on linear OOA(1648, 21847, F16, 12, 12) (dual of [(21847, 12), 262116, 13]-NRT-code), using
(37, 49, 131084)-Net over F16 — Digital
Digital (37, 49, 131084)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1649, 131084, F16, 12) (dual of [131084, 131035, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(1648, 131082, F16, 12) (dual of [131082, 131034, 13]-code), using
- trace code [i] based on linear OA(25624, 65541, F256, 12) (dual of [65541, 65517, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- trace code [i] based on linear OA(25624, 65541, F256, 12) (dual of [65541, 65517, 13]-code), using
- linear OA(1648, 131083, F16, 11) (dual of [131083, 131035, 12]-code), using Gilbert–Varšamov bound and bm = 1648 > Vbs−1(k−1) = 237 921265 851072 487830 179622 045412 398819 429864 575482 003456 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(1648, 131082, F16, 12) (dual of [131082, 131034, 13]-code), using
- construction X with Varšamov bound [i] based on
(37, 49, large)-Net in Base 16 — Upper bound on s
There is no (37, 49, large)-net in base 16, because
- 10 times m-reduction [i] would yield (37, 39, large)-net in base 16, but