Best Known (130−32, 130, s)-Nets in Base 16
(130−32, 130, 8193)-Net over F16 — Constructive and digital
Digital (98, 130, 8193)-net over F16, using
- net defined by OOA [i] based on linear OOA(16130, 8193, F16, 32, 32) (dual of [(8193, 32), 262046, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(16130, 131088, F16, 32) (dual of [131088, 130958, 33]-code), using
- trace code [i] based on linear OA(25665, 65544, F256, 32) (dual of [65544, 65479, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- linear OA(25663, 65536, F256, 32) (dual of [65536, 65473, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- trace code [i] based on linear OA(25665, 65544, F256, 32) (dual of [65544, 65479, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(16130, 131088, F16, 32) (dual of [131088, 130958, 33]-code), using
(130−32, 130, 120880)-Net over F16 — Digital
Digital (98, 130, 120880)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16130, 120880, F16, 32) (dual of [120880, 120750, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(16130, 131088, F16, 32) (dual of [131088, 130958, 33]-code), using
- trace code [i] based on linear OA(25665, 65544, F256, 32) (dual of [65544, 65479, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- linear OA(25663, 65536, F256, 32) (dual of [65536, 65473, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- trace code [i] based on linear OA(25665, 65544, F256, 32) (dual of [65544, 65479, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(16130, 131088, F16, 32) (dual of [131088, 130958, 33]-code), using
(130−32, 130, large)-Net in Base 16 — Upper bound on s
There is no (98, 130, large)-net in base 16, because
- 30 times m-reduction [i] would yield (98, 100, large)-net in base 16, but