Best Known (100, 113, s)-Nets in Base 3
(100, 113, 797161)-Net over F3 — Constructive and digital
Digital (100, 113, 797161)-net over F3, using
- net defined by OOA [i] based on linear OOA(3113, 797161, F3, 13, 13) (dual of [(797161, 13), 10362980, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3113, 4782967, F3, 13) (dual of [4782967, 4782854, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3113, 4782967, F3, 13) (dual of [4782967, 4782854, 14]-code), using
(100, 113, 1406698)-Net over F3 — Digital
Digital (100, 113, 1406698)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3113, 1406698, F3, 3, 13) (dual of [(1406698, 3), 4219981, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3113, 1594323, F3, 3, 13) (dual of [(1594323, 3), 4782856, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(3113, 1594323, F3, 3, 13) (dual of [(1594323, 3), 4782856, 14]-NRT-code), using
(100, 113, large)-Net in Base 3 — Upper bound on s
There is no (100, 113, large)-net in base 3, because
- 11 times m-reduction [i] would yield (100, 102, large)-net in base 3, but