Best Known (152, 152+19, s)-Nets in Base 3
(152, 152+19, 531442)-Net over F3 — Constructive and digital
Digital (152, 171, 531442)-net over F3, using
- 31 times duplication [i] based on digital (151, 170, 531442)-net over F3, using
- net defined by OOA [i] based on linear OOA(3170, 531442, F3, 19, 19) (dual of [(531442, 19), 10097228, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3170, 4782979, F3, 19) (dual of [4782979, 4782809, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3170, 4782984, F3, 19) (dual of [4782984, 4782814, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(3169, 4782969, F3, 19) (dual of [4782969, 4782800, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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(18) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3170, 4782984, F3, 19) (dual of [4782984, 4782814, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3170, 4782979, F3, 19) (dual of [4782979, 4782809, 20]-code), using
- net defined by OOA [i] based on linear OOA(3170, 531442, F3, 19, 19) (dual of [(531442, 19), 10097228, 20]-NRT-code), using
(152, 152+19, 1195746)-Net over F3 — Digital
Digital (152, 171, 1195746)-net over F3, using
- 31 times duplication [i] based on digital (151, 170, 1195746)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3170, 1195746, F3, 4, 19) (dual of [(1195746, 4), 4782814, 20]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3170, 4782984, F3, 19) (dual of [4782984, 4782814, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(3169, 4782969, F3, 19) (dual of [4782969, 4782800, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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(18) ⊂ Ce(16) [i] based on
- OOA 4-folding [i] based on linear OA(3170, 4782984, F3, 19) (dual of [4782984, 4782814, 20]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3170, 1195746, F3, 4, 19) (dual of [(1195746, 4), 4782814, 20]-NRT-code), using
(152, 152+19, large)-Net in Base 3 — Upper bound on s
There is no (152, 171, large)-net in base 3, because
- 17 times m-reduction [i] would yield (152, 154, large)-net in base 3, but