Best Known (105−13, 105, s)-Nets in Base 3
(105−13, 105, 265720)-Net over F3 — Constructive and digital
Digital (92, 105, 265720)-net over F3, using
- net defined by OOA [i] based on linear OOA(3105, 265720, F3, 13, 13) (dual of [(265720, 13), 3454255, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3105, 1594321, F3, 13) (dual of [1594321, 1594216, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3105, 1594321, F3, 13) (dual of [1594321, 1594216, 14]-code), using
(105−13, 105, 529772)-Net over F3 — Digital
Digital (92, 105, 529772)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3105, 529772, F3, 3, 13) (dual of [(529772, 3), 1589211, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3105, 531441, F3, 3, 13) (dual of [(531441, 3), 1594218, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(3105, 531441, F3, 3, 13) (dual of [(531441, 3), 1594218, 14]-NRT-code), using
(105−13, 105, large)-Net in Base 3 — Upper bound on s
There is no (92, 105, large)-net in base 3, because
- 11 times m-reduction [i] would yield (92, 94, large)-net in base 3, but