Best Known (103−22, 103, s)-Nets in Base 9
(103−22, 103, 5371)-Net over F9 — Constructive and digital
Digital (81, 103, 5371)-net over F9, using
- net defined by OOA [i] based on linear OOA(9103, 5371, F9, 22, 22) (dual of [(5371, 22), 118059, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(9103, 59081, F9, 22) (dual of [59081, 58978, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(971, 59049, F9, 16) (dual of [59049, 58978, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(97, 32, F9, 5) (dual of [32, 25, 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(21) ⊂ Ce(15) [i] based on
- OA 11-folding and stacking [i] based on linear OA(9103, 59081, F9, 22) (dual of [59081, 58978, 23]-code), using
(103−22, 103, 59081)-Net over F9 — Digital
Digital (81, 103, 59081)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9103, 59081, F9, 22) (dual of [59081, 58978, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(971, 59049, F9, 16) (dual of [59049, 58978, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(97, 32, F9, 5) (dual of [32, 25, 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(21) ⊂ Ce(15) [i] based on
(103−22, 103, large)-Net in Base 9 — Upper bound on s
There is no (81, 103, large)-net in base 9, because
- 20 times m-reduction [i] would yield (81, 83, large)-net in base 9, but