Best Known (36−8, 36, s)-Nets in Base 9
(36−8, 36, 14763)-Net over F9 — Constructive and digital
Digital (28, 36, 14763)-net over F9, using
- net defined by OOA [i] based on linear OOA(936, 14763, F9, 8, 8) (dual of [(14763, 8), 118068, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(936, 59052, F9, 8) (dual of [59052, 59016, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(936, 59054, F9, 8) (dual of [59054, 59018, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(936, 59049, F9, 8) (dual of [59049, 59013, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(931, 59049, F9, 7) (dual of [59049, 59018, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(936, 59054, F9, 8) (dual of [59054, 59018, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(936, 59052, F9, 8) (dual of [59052, 59016, 9]-code), using
(36−8, 36, 59054)-Net over F9 — Digital
Digital (28, 36, 59054)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(936, 59054, F9, 8) (dual of [59054, 59018, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(936, 59049, F9, 8) (dual of [59049, 59013, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(931, 59049, F9, 7) (dual of [59049, 59018, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(7) ⊂ Ce(6) [i] based on
(36−8, 36, large)-Net in Base 9 — Upper bound on s
There is no (28, 36, large)-net in base 9, because
- 6 times m-reduction [i] would yield (28, 30, large)-net in base 9, but