Best Known (26, 26+22, s)-Nets in Base 128
(26, 26+22, 1491)-Net over F128 — Constructive and digital
Digital (26, 48, 1491)-net over F128, using
- net defined by OOA [i] based on linear OOA(12848, 1491, F128, 22, 22) (dual of [(1491, 22), 32754, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(12848, 16401, F128, 22) (dual of [16401, 16353, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [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(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(1285, 17, F128, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- OA 11-folding and stacking [i] based on linear OA(12848, 16401, F128, 22) (dual of [16401, 16353, 23]-code), using
(26, 26+22, 7881)-Net over F128 — Digital
Digital (26, 48, 7881)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12848, 7881, F128, 2, 22) (dual of [(7881, 2), 15714, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12848, 8200, F128, 2, 22) (dual of [(8200, 2), 16352, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12848, 16400, F128, 22) (dual of [16400, 16352, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12848, 16401, F128, 22) (dual of [16401, 16353, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [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(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(1285, 17, F128, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(12848, 16401, F128, 22) (dual of [16401, 16353, 23]-code), using
- OOA 2-folding [i] based on linear OA(12848, 16400, F128, 22) (dual of [16400, 16352, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(12848, 8200, F128, 2, 22) (dual of [(8200, 2), 16352, 23]-NRT-code), using
(26, 26+22, large)-Net in Base 128 — Upper bound on s
There is no (26, 48, large)-net in base 128, because
- 20 times m-reduction [i] would yield (26, 28, large)-net in base 128, but