Best Known (63−17, 63, s)-Nets in Base 16
(63−17, 63, 8193)-Net over F16 — Constructive and digital
Digital (46, 63, 8193)-net over F16, using
- net defined by OOA [i] based on linear OOA(1663, 8193, F16, 17, 17) (dual of [(8193, 17), 139218, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(1663, 65545, F16, 17) (dual of [65545, 65482, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(1663, 65546, F16, 17) (dual of [65546, 65483, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(1661, 65536, F16, 17) (dual of [65536, 65475, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1653, 65536, F16, 14) (dual of [65536, 65483, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(162, 10, F16, 2) (dual of [10, 8, 3]-code or 10-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(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(1663, 65546, F16, 17) (dual of [65546, 65483, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(1663, 65545, F16, 17) (dual of [65545, 65482, 18]-code), using
(63−17, 63, 40609)-Net over F16 — Digital
Digital (46, 63, 40609)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1663, 40609, F16, 17) (dual of [40609, 40546, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(1663, 65546, F16, 17) (dual of [65546, 65483, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(1661, 65536, F16, 17) (dual of [65536, 65475, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1653, 65536, F16, 14) (dual of [65536, 65483, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(162, 10, F16, 2) (dual of [10, 8, 3]-code or 10-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(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(1663, 65546, F16, 17) (dual of [65546, 65483, 18]-code), using
(63−17, 63, large)-Net in Base 16 — Upper bound on s
There is no (46, 63, large)-net in base 16, because
- 15 times m-reduction [i] would yield (46, 48, large)-net in base 16, but