Best Known (100, 100+16, s)-Nets in Base 3
(100, 100+16, 22146)-Net over F3 — Constructive and digital
Digital (100, 116, 22146)-net over F3, using
- 31 times duplication [i] based on digital (99, 115, 22146)-net over F3, using
- net defined by OOA [i] based on linear OOA(3115, 22146, F3, 16, 16) (dual of [(22146, 16), 354221, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3115, 177168, F3, 16) (dual of [177168, 177053, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3115, 177173, F3, 16) (dual of [177173, 177058, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(389, 177147, F3, 13) (dual of [177147, 177058, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(34, 26, F3, 2) (dual of [26, 22, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3115, 177173, F3, 16) (dual of [177173, 177058, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3115, 177168, F3, 16) (dual of [177168, 177053, 17]-code), using
- net defined by OOA [i] based on linear OOA(3115, 22146, F3, 16, 16) (dual of [(22146, 16), 354221, 17]-NRT-code), using
(100, 100+16, 59058)-Net over F3 — Digital
Digital (100, 116, 59058)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3116, 59058, F3, 3, 16) (dual of [(59058, 3), 177058, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3116, 177174, F3, 16) (dual of [177174, 177058, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3115, 177173, F3, 16) (dual of [177173, 177058, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(389, 177147, F3, 13) (dual of [177147, 177058, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(34, 26, F3, 2) (dual of [26, 22, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3115, 177173, F3, 16) (dual of [177173, 177058, 17]-code), using
- OOA 3-folding [i] based on linear OA(3116, 177174, F3, 16) (dual of [177174, 177058, 17]-code), using
(100, 100+16, large)-Net in Base 3 — Upper bound on s
There is no (100, 116, large)-net in base 3, because
- 14 times m-reduction [i] would yield (100, 102, large)-net in base 3, but