Best Known (26, 49, s)-Nets in Base 128
(26, 49, 1490)-Net over F128 — Constructive and digital
Digital (26, 49, 1490)-net over F128, using
- 1282 times duplication [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
(26, 49, 5845)-Net over F128 — Digital
Digital (26, 49, 5845)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12849, 5845, F128, 2, 23) (dual of [(5845, 2), 11641, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12849, 8199, F128, 2, 23) (dual of [(8199, 2), 16349, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12849, 16398, F128, 23) (dual of [16398, 16349, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [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(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(22) ⊂ Ce(17) [i] based on
- OOA 2-folding [i] based on linear OA(12849, 16398, F128, 23) (dual of [16398, 16349, 24]-code), using
- discarding factors / shortening the dual code based on linear OOA(12849, 8199, F128, 2, 23) (dual of [(8199, 2), 16349, 24]-NRT-code), using
(26, 49, large)-Net in Base 128 — Upper bound on s
There is no (26, 49, large)-net in base 128, because
- 21 times m-reduction [i] would yield (26, 28, large)-net in base 128, but