Best Known (47, 47+14, s)-Nets in Base 9
(47, 47+14, 8436)-Net over F9 — Constructive and digital
Digital (47, 61, 8436)-net over F9, using
- net defined by OOA [i] based on linear OOA(961, 8436, F9, 14, 14) (dual of [(8436, 14), 118043, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(961, 59052, F9, 14) (dual of [59052, 58991, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(961, 59054, F9, 14) (dual of [59054, 58993, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(961, 59049, F9, 14) (dual of [59049, 58988, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(956, 59049, F9, 13) (dual of [59049, 58993, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(90, 5, F9, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(961, 59054, F9, 14) (dual of [59054, 58993, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(961, 59052, F9, 14) (dual of [59052, 58991, 15]-code), using
(47, 47+14, 39031)-Net over F9 — Digital
Digital (47, 61, 39031)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(961, 39031, F9, 14) (dual of [39031, 38970, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(961, 59049, F9, 14) (dual of [59049, 58988, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(961, 59049, F9, 14) (dual of [59049, 58988, 15]-code), using
(47, 47+14, large)-Net in Base 9 — Upper bound on s
There is no (47, 61, large)-net in base 9, because
- 12 times m-reduction [i] would yield (47, 49, large)-net in base 9, but