Best Known (133−21, 133, s)-Nets in Base 9
(133−21, 133, 478300)-Net over F9 — Constructive and digital
Digital (112, 133, 478300)-net over F9, using
- net defined by OOA [i] based on linear OOA(9133, 478300, F9, 21, 21) (dual of [(478300, 21), 10044167, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(9133, 4783001, F9, 21) (dual of [4783001, 4782868, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(9133, 4783003, F9, 21) (dual of [4783003, 4782870, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(9127, 4782969, F9, 21) (dual of [4782969, 4782842, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 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(96, 34, F9, 4) (dual of [34, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(9133, 4783003, F9, 21) (dual of [4783003, 4782870, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(9133, 4783001, F9, 21) (dual of [4783001, 4782868, 22]-code), using
(133−21, 133, 4222782)-Net over F9 — Digital
Digital (112, 133, 4222782)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9133, 4222782, F9, 21) (dual of [4222782, 4222649, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(9133, 4783003, F9, 21) (dual of [4783003, 4782870, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(9127, 4782969, F9, 21) (dual of [4782969, 4782842, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 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(96, 34, F9, 4) (dual of [34, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(9133, 4783003, F9, 21) (dual of [4783003, 4782870, 22]-code), using
(133−21, 133, large)-Net in Base 9 — Upper bound on s
There is no (112, 133, large)-net in base 9, because
- 19 times m-reduction [i] would yield (112, 114, large)-net in base 9, but