Best Known (90, 90+16, s)-Nets in Base 9
(90, 90+16, 597877)-Net over F9 — Constructive and digital
Digital (90, 106, 597877)-net over F9, using
- net defined by OOA [i] based on linear OOA(9106, 597877, F9, 16, 16) (dual of [(597877, 16), 9565926, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(9106, 4783016, F9, 16) (dual of [4783016, 4782910, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(9106, 4783018, F9, 16) (dual of [4783018, 4782912, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [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(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(97, 49, F9, 5) (dual of [49, 42, 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(15) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(9106, 4783018, F9, 16) (dual of [4783018, 4782912, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(9106, 4783016, F9, 16) (dual of [4783016, 4782910, 17]-code), using
(90, 90+16, 4783018)-Net over F9 — Digital
Digital (90, 106, 4783018)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9106, 4783018, F9, 16) (dual of [4783018, 4782912, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [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(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(97, 49, F9, 5) (dual of [49, 42, 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(15) ⊂ Ce(9) [i] based on
(90, 90+16, large)-Net in Base 9 — Upper bound on s
There is no (90, 106, large)-net in base 9, because
- 14 times m-reduction [i] would yield (90, 92, large)-net in base 9, but