Best Known (35, 35+11, s)-Nets in Base 16
(35, 35+11, 26217)-Net over F16 — Constructive and digital
Digital (35, 46, 26217)-net over F16, using
- net defined by OOA [i] based on linear OOA(1646, 26217, F16, 11, 11) (dual of [(26217, 11), 288341, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(1646, 131086, F16, 11) (dual of [131086, 131040, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(1646, 131088, F16, 11) (dual of [131088, 131042, 12]-code), using
- trace code [i] based on linear OA(25623, 65544, F256, 11) (dual of [65544, 65521, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(10) ⊂ Ce(7) [i] based on
- trace code [i] based on linear OA(25623, 65544, F256, 11) (dual of [65544, 65521, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(1646, 131088, F16, 11) (dual of [131088, 131042, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(1646, 131086, F16, 11) (dual of [131086, 131040, 12]-code), using
(35, 35+11, 131088)-Net over F16 — Digital
Digital (35, 46, 131088)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1646, 131088, F16, 11) (dual of [131088, 131042, 12]-code), using
- trace code [i] based on linear OA(25623, 65544, F256, 11) (dual of [65544, 65521, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(10) ⊂ Ce(7) [i] based on
- trace code [i] based on linear OA(25623, 65544, F256, 11) (dual of [65544, 65521, 12]-code), using
(35, 35+11, large)-Net in Base 16 — Upper bound on s
There is no (35, 46, large)-net in base 16, because
- 9 times m-reduction [i] would yield (35, 37, large)-net in base 16, but