Best Known (26, 46, s)-Nets in Base 128
(26, 46, 1640)-Net over F128 — Constructive and digital
Digital (26, 46, 1640)-net over F128, using
- t-expansion [i] based on digital (25, 46, 1640)-net over F128, using
- net defined by OOA [i] based on linear OOA(12846, 1640, F128, 21, 21) (dual of [(1640, 21), 34394, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(12846, 16401, F128, 21) (dual of [16401, 16355, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(12846, 16402, F128, 21) (dual of [16402, 16356, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- linear OA(12841, 16385, F128, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(12829, 16385, F128, 15) (dual of [16385, 16356, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [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 C([0,10]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12846, 16402, F128, 21) (dual of [16402, 16356, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(12846, 16401, F128, 21) (dual of [16401, 16355, 22]-code), using
- net defined by OOA [i] based on linear OOA(12846, 1640, F128, 21, 21) (dual of [(1640, 21), 34394, 22]-NRT-code), using
(26, 46, 6554)-Net in Base 128 — Constructive
(26, 46, 6554)-net in base 128, using
- net defined by OOA [i] based on OOA(12846, 6554, S128, 20, 20), using
- OA 10-folding and stacking [i] based on OA(12846, 65540, S128, 20), using
- discarding factors based on OA(12846, 65541, S128, 20), using
- discarding parts of the base [i] based on linear OA(25640, 65541, F256, 20) (dual of [65541, 65501, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- discarding parts of the base [i] based on linear OA(25640, 65541, F256, 20) (dual of [65541, 65501, 21]-code), using
- discarding factors based on OA(12846, 65541, S128, 20), using
- OA 10-folding and stacking [i] based on OA(12846, 65540, S128, 20), using
(26, 46, 11016)-Net over F128 — Digital
Digital (26, 46, 11016)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12846, 11016, F128, 20) (dual of [11016, 10970, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12846, 16407, F128, 20) (dual of [16407, 16361, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(11) [i] based on
- 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(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1287, 23, F128, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- construction X applied to Ce(19) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(12846, 16407, F128, 20) (dual of [16407, 16361, 21]-code), using
(26, 46, large)-Net in Base 128 — Upper bound on s
There is no (26, 46, large)-net in base 128, because
- 18 times m-reduction [i] would yield (26, 28, large)-net in base 128, but