Best Known (80, 80+19, s)-Nets in Base 9
(80, 80+19, 59050)-Net over F9 — Constructive and digital
Digital (80, 99, 59050)-net over F9, using
- net defined by OOA [i] based on linear OOA(999, 59050, F9, 19, 19) (dual of [(59050, 19), 1121851, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(999, 531451, F9, 19) (dual of [531451, 531352, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- OOA 9-folding and stacking with additional row [i] based on linear OA(999, 531451, F9, 19) (dual of [531451, 531352, 20]-code), using
(80, 80+19, 284294)-Net over F9 — Digital
Digital (80, 99, 284294)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(999, 284294, F9, 19) (dual of [284294, 284195, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(999, 531451, F9, 19) (dual of [531451, 531352, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(999, 531451, F9, 19) (dual of [531451, 531352, 20]-code), using
(80, 80+19, large)-Net in Base 9 — Upper bound on s
There is no (80, 99, large)-net in base 9, because
- 17 times m-reduction [i] would yield (80, 82, large)-net in base 9, but