Best Known (106, 122, s)-Nets in Base 3
(106, 122, 66431)-Net over F3 — Constructive and digital
Digital (106, 122, 66431)-net over F3, using
- net defined by OOA [i] based on linear OOA(3122, 66431, F3, 16, 16) (dual of [(66431, 16), 1062774, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3122, 531448, F3, 16) (dual of [531448, 531326, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3122, 531454, F3, 16) (dual of [531454, 531332, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3122, 531454, F3, 16) (dual of [531454, 531332, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3122, 531448, F3, 16) (dual of [531448, 531326, 17]-code), using
(106, 122, 142479)-Net over F3 — Digital
Digital (106, 122, 142479)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3122, 142479, F3, 3, 16) (dual of [(142479, 3), 427315, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3122, 177151, F3, 3, 16) (dual of [(177151, 3), 531331, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3122, 531453, F3, 16) (dual of [531453, 531331, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3122, 531454, F3, 16) (dual of [531454, 531332, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3122, 531454, F3, 16) (dual of [531454, 531332, 17]-code), using
- OOA 3-folding [i] based on linear OA(3122, 531453, F3, 16) (dual of [531453, 531331, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(3122, 177151, F3, 3, 16) (dual of [(177151, 3), 531331, 17]-NRT-code), using
(106, 122, large)-Net in Base 3 — Upper bound on s
There is no (106, 122, large)-net in base 3, because
- 14 times m-reduction [i] would yield (106, 108, large)-net in base 3, but