Best Known (12, 23, s)-Nets in Base 128
(12, 23, 3278)-Net over F128 — Constructive and digital
Digital (12, 23, 3278)-net over F128, using
- net defined by OOA [i] based on linear OOA(12823, 3278, F128, 11, 11) (dual of [(3278, 11), 36035, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12823, 16391, F128, 11) (dual of [16391, 16368, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(12823, 16392, F128, 11) (dual of [16392, 16369, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(12821, 16384, F128, 11) (dual of [16384, 16363, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(12815, 16384, F128, 8) (dual of [16384, 16369, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(10) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(12823, 16392, F128, 11) (dual of [16392, 16369, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12823, 16391, F128, 11) (dual of [16391, 16368, 12]-code), using
(12, 23, 8196)-Net over F128 — Digital
Digital (12, 23, 8196)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12823, 8196, F128, 2, 11) (dual of [(8196, 2), 16369, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12823, 16392, F128, 11) (dual of [16392, 16369, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(12821, 16384, F128, 11) (dual of [16384, 16363, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(12815, 16384, F128, 8) (dual of [16384, 16369, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(10) ⊂ Ce(7) [i] based on
- OOA 2-folding [i] based on linear OA(12823, 16392, F128, 11) (dual of [16392, 16369, 12]-code), using
(12, 23, large)-Net in Base 128 — Upper bound on s
There is no (12, 23, large)-net in base 128, because
- 9 times m-reduction [i] would yield (12, 14, large)-net in base 128, but