Best Known (103−16, 103, s)-Nets in Base 9
(103−16, 103, 597875)-Net over F9 — Constructive and digital
Digital (87, 103, 597875)-net over F9, using
- net defined by OOA [i] based on linear OOA(9103, 597875, F9, 16, 16) (dual of [(597875, 16), 9565897, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(9103, 4783000, F9, 16) (dual of [4783000, 4782897, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(9103, 4783001, F9, 16) (dual of [4783001, 4782898, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(9103, 4783001, F9, 16) (dual of [4783001, 4782898, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(9103, 4783000, F9, 16) (dual of [4783000, 4782897, 17]-code), using
(103−16, 103, 4783001)-Net over F9 — Digital
Digital (87, 103, 4783001)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9103, 4783001, F9, 16) (dual of [4783001, 4782898, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
(103−16, 103, large)-Net in Base 9 — Upper bound on s
There is no (87, 103, large)-net in base 9, because
- 14 times m-reduction [i] would yield (87, 89, large)-net in base 9, but