Best Known (54−11, 54, s)-Nets in Base 8
(54−11, 54, 6583)-Net over F8 — Constructive and digital
Digital (43, 54, 6583)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 28)-net over F8, using
- net defined by OOA [i] based on linear OOA(87, 28, F8, 5, 5) (dual of [(28, 5), 133, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- net defined by OOA [i] based on linear OOA(87, 28, F8, 5, 5) (dual of [(28, 5), 133, 6]-NRT-code), using
- 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
- net defined by OOA [i] based on linear OOA(847, 6555, F8, 11, 11) (dual of [(6555, 11), 72058, 12]-NRT-code), using
- digital (2, 7, 28)-net over F8, using
(54−11, 54, 48709)-Net over F8 — Digital
Digital (43, 54, 48709)-net over F8, using
(54−11, 54, large)-Net in Base 8 — Upper bound on s
There is no (43, 54, large)-net in base 8, because
- 9 times m-reduction [i] would yield (43, 45, large)-net in base 8, but