Best Known (95, 95+34, s)-Nets in Base 16
(95, 95+34, 3856)-Net over F16 — Constructive and digital
Digital (95, 129, 3856)-net over F16, using
- net defined by OOA [i] based on linear OOA(16129, 3856, F16, 34, 34) (dual of [(3856, 34), 130975, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(16129, 65552, F16, 34) (dual of [65552, 65423, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(16129, 65553, F16, 34) (dual of [65553, 65424, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(16109, 65536, F16, 29) (dual of [65536, 65427, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(164, 17, F16, 4) (dual of [17, 13, 5]-code or 17-arc in PG(3,16)), using
- extended Reed–Solomon code RSe(13,16) [i]
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(16129, 65553, F16, 34) (dual of [65553, 65424, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(16129, 65552, F16, 34) (dual of [65552, 65423, 35]-code), using
(95, 95+34, 55865)-Net over F16 — Digital
Digital (95, 129, 55865)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16129, 55865, F16, 34) (dual of [55865, 55736, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(16129, 65553, F16, 34) (dual of [65553, 65424, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(16109, 65536, F16, 29) (dual of [65536, 65427, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(164, 17, F16, 4) (dual of [17, 13, 5]-code or 17-arc in PG(3,16)), using
- extended Reed–Solomon code RSe(13,16) [i]
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(16129, 65553, F16, 34) (dual of [65553, 65424, 35]-code), using
(95, 95+34, large)-Net in Base 16 — Upper bound on s
There is no (95, 129, large)-net in base 16, because
- 32 times m-reduction [i] would yield (95, 97, large)-net in base 16, but