Best Known (148−15, 148, s)-Nets in Base 3
(148−15, 148, 683288)-Net over F3 — Constructive and digital
Digital (133, 148, 683288)-net over F3, using
- 31 times duplication [i] based on digital (132, 147, 683288)-net over F3, using
- net defined by OOA [i] based on linear OOA(3147, 683288, F3, 15, 15) (dual of [(683288, 15), 10249173, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3147, 4783017, F3, 15) (dual of [4783017, 4782870, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(3147, 4783017, F3, 15) (dual of [4783017, 4782870, 16]-code), using
- net defined by OOA [i] based on linear OOA(3147, 683288, F3, 15, 15) (dual of [(683288, 15), 10249173, 16]-NRT-code), using
(148−15, 148, 1687733)-Net over F3 — Digital
Digital (133, 148, 1687733)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3148, 1687733, F3, 2, 15) (dual of [(1687733, 2), 3375318, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3148, 2391509, F3, 2, 15) (dual of [(2391509, 2), 4782870, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3148, 4783018, F3, 15) (dual of [4783018, 4782870, 16]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3147, 4783017, F3, 15) (dual of [4783017, 4782870, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3147, 4783017, F3, 15) (dual of [4783017, 4782870, 16]-code), using
- OOA 2-folding [i] based on linear OA(3148, 4783018, F3, 15) (dual of [4783018, 4782870, 16]-code), using
- discarding factors / shortening the dual code based on linear OOA(3148, 2391509, F3, 2, 15) (dual of [(2391509, 2), 4782870, 16]-NRT-code), using
(148−15, 148, large)-Net in Base 3 — Upper bound on s
There is no (133, 148, large)-net in base 3, because
- 13 times m-reduction [i] would yield (133, 135, large)-net in base 3, but