Best Known (38, 38+28, s)-Nets in Base 128
(38, 38+28, 1172)-Net over F128 — Constructive and digital
Digital (38, 66, 1172)-net over F128, using
- 1281 times duplication [i] based on digital (37, 65, 1172)-net over F128, using
- t-expansion [i] based on digital (36, 65, 1172)-net over F128, using
- net defined by OOA [i] based on linear OOA(12865, 1172, F128, 29, 29) (dual of [(1172, 29), 33923, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12865, 16409, F128, 29) (dual of [16409, 16344, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(12865, 16410, F128, 29) (dual of [16410, 16345, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(19) [i] based on
- linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(1288, 26, F128, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,128)), using
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), using
- Reed–Solomon code RS(120,128) [i]
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), using
- construction X applied to Ce(28) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(12865, 16410, F128, 29) (dual of [16410, 16345, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12865, 16409, F128, 29) (dual of [16409, 16344, 30]-code), using
- net defined by OOA [i] based on linear OOA(12865, 1172, F128, 29, 29) (dual of [(1172, 29), 33923, 30]-NRT-code), using
- t-expansion [i] based on digital (36, 65, 1172)-net over F128, using
(38, 38+28, 4681)-Net in Base 128 — Constructive
(38, 66, 4681)-net in base 128, using
- t-expansion [i] based on (37, 66, 4681)-net in base 128, using
- net defined by OOA [i] based on OOA(12866, 4681, S128, 29, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(12866, 65535, S128, 29), using
- discarding factors based on OA(12866, 65538, S128, 29), using
- discarding parts of the base [i] based on linear OA(25657, 65538, F256, 29) (dual of [65538, 65481, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- discarding parts of the base [i] based on linear OA(25657, 65538, F256, 29) (dual of [65538, 65481, 30]-code), using
- discarding factors based on OA(12866, 65538, S128, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(12866, 65535, S128, 29), using
- net defined by OOA [i] based on OOA(12866, 4681, S128, 29, 29), using
(38, 38+28, 15388)-Net over F128 — Digital
Digital (38, 66, 15388)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12866, 15388, F128, 28) (dual of [15388, 15322, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(12866, 16419, F128, 28) (dual of [16419, 16353, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(15) [i] based on
- linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(12811, 35, F128, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,128)), using
- discarding factors / shortening the dual code based on linear OA(12811, 128, F128, 11) (dual of [128, 117, 12]-code or 128-arc in PG(10,128)), using
- Reed–Solomon code RS(117,128) [i]
- discarding factors / shortening the dual code based on linear OA(12811, 128, F128, 11) (dual of [128, 117, 12]-code or 128-arc in PG(10,128)), using
- construction X applied to Ce(27) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(12866, 16419, F128, 28) (dual of [16419, 16353, 29]-code), using
(38, 38+28, large)-Net in Base 128 — Upper bound on s
There is no (38, 66, large)-net in base 128, because
- 26 times m-reduction [i] would yield (38, 40, large)-net in base 128, but