Best Known (47−22, 47, s)-Nets in Base 128
(47−22, 47, 1490)-Net over F128 — Constructive and digital
Digital (25, 47, 1490)-net over F128, using
- t-expansion [i] based on digital (24, 47, 1490)-net over F128, using
- net defined by OOA [i] based on linear OOA(12847, 1490, F128, 23, 23) (dual of [(1490, 23), 34223, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12847, 16391, F128, 23) (dual of [16391, 16344, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(12847, 16392, F128, 23) (dual of [16392, 16345, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(12845, 16384, F128, 23) (dual of [16384, 16339, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(12847, 16392, F128, 23) (dual of [16392, 16345, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12847, 16391, F128, 23) (dual of [16391, 16344, 24]-code), using
- net defined by OOA [i] based on linear OOA(12847, 1490, F128, 23, 23) (dual of [(1490, 23), 34223, 24]-NRT-code), using
(47−22, 47, 6103)-Net over F128 — Digital
Digital (25, 47, 6103)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12847, 6103, F128, 2, 22) (dual of [(6103, 2), 12159, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12847, 8199, F128, 2, 22) (dual of [(8199, 2), 16351, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12847, 16398, F128, 22) (dual of [16398, 16351, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12833, 16384, F128, 17) (dual of [16384, 16351, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1284, 14, F128, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- OOA 2-folding [i] based on linear OA(12847, 16398, F128, 22) (dual of [16398, 16351, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(12847, 8199, F128, 2, 22) (dual of [(8199, 2), 16351, 23]-NRT-code), using
(47−22, 47, large)-Net in Base 128 — Upper bound on s
There is no (25, 47, large)-net in base 128, because
- 20 times m-reduction [i] would yield (25, 27, large)-net in base 128, but