Best Known (84, 102, s)-Nets in Base 9
(84, 102, 59052)-Net over F9 — Constructive and digital
Digital (84, 102, 59052)-net over F9, using
- 1 times m-reduction [i] based on digital (84, 103, 59052)-net over F9, using
- net defined by OOA [i] based on linear OOA(9103, 59052, F9, 19, 19) (dual of [(59052, 19), 1121885, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9103, 531469, F9, 19) (dual of [531469, 531366, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9103, 531471, F9, 19) (dual of [531471, 531368, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(973, 531441, F9, 14) (dual of [531441, 531368, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(96, 30, F9, 4) (dual of [30, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(9103, 531471, F9, 19) (dual of [531471, 531368, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9103, 531469, F9, 19) (dual of [531469, 531366, 20]-code), using
- net defined by OOA [i] based on linear OOA(9103, 59052, F9, 19, 19) (dual of [(59052, 19), 1121885, 20]-NRT-code), using
(84, 102, 531471)-Net over F9 — Digital
Digital (84, 102, 531471)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9102, 531471, F9, 18) (dual of [531471, 531369, 19]-code), using
- construction XX applied to Ce(18) ⊂ Ce(13) ⊂ Ce(12) [i] based on
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(973, 531441, F9, 14) (dual of [531441, 531368, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(967, 531441, F9, 13) (dual of [531441, 531374, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(94, 29, F9, 3) (dual of [29, 25, 4]-code or 29-cap in PG(3,9)), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(18) ⊂ Ce(13) ⊂ Ce(12) [i] based on
(84, 102, large)-Net in Base 9 — Upper bound on s
There is no (84, 102, large)-net in base 9, because
- 16 times m-reduction [i] would yield (84, 86, large)-net in base 9, but