Best Known (120−19, 120, s)-Nets in Base 9
(120−19, 120, 531445)-Net over F9 — Constructive and digital
Digital (101, 120, 531445)-net over F9, using
- net defined by OOA [i] based on linear OOA(9120, 531445, F9, 19, 19) (dual of [(531445, 19), 10097335, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9120, 4783006, F9, 19) (dual of [4783006, 4782886, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9120, 4783011, F9, 19) (dual of [4783011, 4782891, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(97, 42, F9, 5) (dual of [42, 35, 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(18) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(9120, 4783011, F9, 19) (dual of [4783011, 4782891, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9120, 4783006, F9, 19) (dual of [4783006, 4782886, 20]-code), using
(120−19, 120, 4290934)-Net over F9 — Digital
Digital (101, 120, 4290934)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9120, 4290934, F9, 19) (dual of [4290934, 4290814, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9120, 4783005, F9, 19) (dual of [4783005, 4782885, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(985, 4782970, F9, 13) (dual of [4782970, 4782885, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(97, 35, F9, 5) (dual of [35, 28, 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 C([0,9]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(9120, 4783005, F9, 19) (dual of [4783005, 4782885, 20]-code), using
(120−19, 120, large)-Net in Base 9 — Upper bound on s
There is no (101, 120, large)-net in base 9, because
- 17 times m-reduction [i] would yield (101, 103, large)-net in base 9, but