Best Known (148, 161, s)-Nets in Base 3
(148, 161, 1594328)-Net over F3 — Constructive and digital
Digital (148, 161, 1594328)-net over F3, using
- 31 times duplication [i] based on digital (147, 160, 1594328)-net over F3, using
- net defined by OOA [i] based on linear OOA(3160, 1594328, F3, 14, 13) (dual of [(1594328, 14), 22320432, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3160, 4782985, F3, 2, 13) (dual of [(4782985, 2), 9565810, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3160, 4782986, F3, 2, 13) (dual of [(4782986, 2), 9565812, 14]-NRT-code), using
- trace code [i] based on linear OOA(980, 2391493, F9, 2, 13) (dual of [(2391493, 2), 4782906, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(980, 4782986, F9, 13) (dual of [4782986, 4782906, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(979, 4782985, F9, 13) (dual of [4782985, 4782906, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(964, 4782969, F9, 11) (dual of [4782969, 4782905, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(915, 16, F9, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,9)), using
- dual of repetition code with length 16 [i]
- linear OA(91, 16, F9, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(979, 4782985, F9, 13) (dual of [4782985, 4782906, 14]-code), using
- OOA 2-folding [i] based on linear OA(980, 4782986, F9, 13) (dual of [4782986, 4782906, 14]-code), using
- trace code [i] based on linear OOA(980, 2391493, F9, 2, 13) (dual of [(2391493, 2), 4782906, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3160, 4782986, F3, 2, 13) (dual of [(4782986, 2), 9565812, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3160, 4782985, F3, 2, 13) (dual of [(4782985, 2), 9565810, 14]-NRT-code), using
- net defined by OOA [i] based on linear OOA(3160, 1594328, F3, 14, 13) (dual of [(1594328, 14), 22320432, 14]-NRT-code), using
(148, 161, large)-Net over F3 — Digital
Digital (148, 161, large)-net over F3, using
- 39 times duplication [i] based on digital (139, 152, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3152, large, F3, 13) (dual of [large, large−152, 14]-code), using
- 31 times code embedding in larger space [i] based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 31 times code embedding in larger space [i] based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3152, large, F3, 13) (dual of [large, large−152, 14]-code), using
(148, 161, large)-Net in Base 3 — Upper bound on s
There is no (148, 161, large)-net in base 3, because
- 11 times m-reduction [i] would yield (148, 150, large)-net in base 3, but