Best Known (102−19, 102, s)-Nets in Base 9
(102−19, 102, 59051)-Net over F9 — Constructive and digital
Digital (83, 102, 59051)-net over F9, using
- 91 times duplication [i] based on digital (82, 101, 59051)-net over F9, using
- net defined by OOA [i] based on linear OOA(9101, 59051, F9, 19, 19) (dual of [(59051, 19), 1121868, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9101, 531460, F9, 19) (dual of [531460, 531359, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9101, 531463, F9, 19) (dual of [531463, 531362, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [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(979, 531441, F9, 15) (dual of [531441, 531362, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(94, 22, F9, 3) (dual of [22, 18, 4]-code or 22-cap in PG(3,9)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(9101, 531463, F9, 19) (dual of [531463, 531362, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9101, 531460, F9, 19) (dual of [531460, 531359, 20]-code), using
- net defined by OOA [i] based on linear OOA(9101, 59051, F9, 19, 19) (dual of [(59051, 19), 1121868, 20]-NRT-code), using
(102−19, 102, 418956)-Net over F9 — Digital
Digital (83, 102, 418956)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9102, 418956, F9, 19) (dual of [418956, 418854, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9102, 531465, F9, 19) (dual of [531465, 531363, 20]-code), using
- construction XX applied to Ce(18) ⊂ Ce(14) ⊂ 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(979, 531441, F9, 15) (dual of [531441, 531362, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(94, 23, F9, 3) (dual of [23, 19, 4]-code or 23-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(14) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(9102, 531465, F9, 19) (dual of [531465, 531363, 20]-code), using
(102−19, 102, large)-Net in Base 9 — Upper bound on s
There is no (83, 102, large)-net in base 9, because
- 17 times m-reduction [i] would yield (83, 85, large)-net in base 9, but