Best Known (47−11, 47, s)-Nets in Base 8
(47−11, 47, 6555)-Net over F8 — Constructive and digital
Digital (36, 47, 6555)-net over F8, using
- net defined by OOA [i] based on linear OOA(847, 6555, F8, 11, 11) (dual of [(6555, 11), 72058, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(847, 32776, F8, 11) (dual of [32776, 32729, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(847, 32779, F8, 11) (dual of [32779, 32732, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(846, 32768, F8, 11) (dual of [32768, 32722, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(847, 32779, F8, 11) (dual of [32779, 32732, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(847, 32776, F8, 11) (dual of [32776, 32729, 12]-code), using
(47−11, 47, 24455)-Net over F8 — Digital
Digital (36, 47, 24455)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(847, 24455, F8, 11) (dual of [24455, 24408, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(847, 32779, F8, 11) (dual of [32779, 32732, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(846, 32768, F8, 11) (dual of [32768, 32722, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(847, 32779, F8, 11) (dual of [32779, 32732, 12]-code), using
(47−11, 47, large)-Net in Base 8 — Upper bound on s
There is no (36, 47, large)-net in base 8, because
- 9 times m-reduction [i] would yield (36, 38, large)-net in base 8, but