Best Known (36, 36+12, s)-Nets in Base 16
(36, 36+12, 21847)-Net over F16 — Constructive and digital
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
(36, 36+12, 131082)-Net over F16 — Digital
Digital (36, 48, 131082)-net over F16, using
- embedding of OOA with Gilbert–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
(36, 36+12, large)-Net in Base 16 — Upper bound on s
There is no (36, 48, large)-net in base 16, because
- 10 times m-reduction [i] would yield (36, 38, large)-net in base 16, but