Best Known (100−18, 100, s)-Nets in Base 9
(100−18, 100, 59051)-Net over F9 — Constructive and digital
Digital (82, 100, 59051)-net over F9, using
- net defined by OOA [i] based on linear OOA(9100, 59051, F9, 18, 18) (dual of [(59051, 18), 1062818, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(9100, 531459, F9, 18) (dual of [531459, 531359, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(9100, 531462, F9, 18) (dual of [531462, 531362, 19]-code), using
- 1 times truncation [i] 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
- 1 times truncation [i] based on linear OA(9101, 531463, F9, 19) (dual of [531463, 531362, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9100, 531462, F9, 18) (dual of [531462, 531362, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(9100, 531459, F9, 18) (dual of [531459, 531359, 19]-code), using
(100−18, 100, 531462)-Net over F9 — Digital
Digital (82, 100, 531462)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9100, 531462, F9, 18) (dual of [531462, 531362, 19]-code), using
- 1 times truncation [i] 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
- 1 times truncation [i] based on linear OA(9101, 531463, F9, 19) (dual of [531463, 531362, 20]-code), using
(100−18, 100, large)-Net in Base 9 — Upper bound on s
There is no (82, 100, large)-net in base 9, because
- 16 times m-reduction [i] would yield (82, 84, large)-net in base 9, but