Best Known (84−22, 84, s)-Nets in Base 16
(84−22, 84, 5959)-Net over F16 — Constructive and digital
Digital (62, 84, 5959)-net over F16, using
- 161 times duplication [i] based on digital (61, 83, 5959)-net over F16, using
- net defined by OOA [i] based on linear OOA(1683, 5959, F16, 22, 22) (dual of [(5959, 22), 131015, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(1683, 65549, F16, 22) (dual of [65549, 65466, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(1683, 65550, F16, 22) (dual of [65550, 65467, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(1681, 65536, F16, 22) (dual of [65536, 65455, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1669, 65536, F16, 19) (dual of [65536, 65467, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(1683, 65550, F16, 22) (dual of [65550, 65467, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(1683, 65549, F16, 22) (dual of [65549, 65466, 23]-code), using
- net defined by OOA [i] based on linear OOA(1683, 5959, F16, 22, 22) (dual of [(5959, 22), 131015, 23]-NRT-code), using
(84−22, 84, 54983)-Net over F16 — Digital
Digital (62, 84, 54983)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1684, 54983, F16, 22) (dual of [54983, 54899, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(1684, 65554, F16, 22) (dual of [65554, 65470, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(1681, 65536, F16, 22) (dual of [65536, 65455, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1665, 65536, F16, 18) (dual of [65536, 65471, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(1684, 65554, F16, 22) (dual of [65554, 65470, 23]-code), using
(84−22, 84, large)-Net in Base 16 — Upper bound on s
There is no (62, 84, large)-net in base 16, because
- 20 times m-reduction [i] would yield (62, 64, large)-net in base 16, but