Best Known (100, 100+22, s)-Nets in Base 9
(100, 100+22, 48316)-Net over F9 — Constructive and digital
Digital (100, 122, 48316)-net over F9, using
- net defined by OOA [i] based on linear OOA(9122, 48316, F9, 22, 22) (dual of [(48316, 22), 1062830, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(9122, 531476, F9, 22) (dual of [531476, 531354, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(9122, 531478, F9, 22) (dual of [531478, 531356, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(985, 531441, F9, 16) (dual of [531441, 531356, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(97, 37, F9, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(9122, 531478, F9, 22) (dual of [531478, 531356, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(9122, 531476, F9, 22) (dual of [531476, 531354, 23]-code), using
(100, 100+22, 531478)-Net over F9 — Digital
Digital (100, 122, 531478)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9122, 531478, F9, 22) (dual of [531478, 531356, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(985, 531441, F9, 16) (dual of [531441, 531356, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(97, 37, F9, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
(100, 100+22, large)-Net in Base 9 — Upper bound on s
There is no (100, 122, large)-net in base 9, because
- 20 times m-reduction [i] would yield (100, 102, large)-net in base 9, but