Best Known (147, 147+17, s)-Nets in Base 3
(147, 147+17, 597879)-Net over F3 — Constructive and digital
Digital (147, 164, 597879)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (138, 155, 597872)-net over F3, using
- net defined by OOA [i] based on linear OOA(3155, 597872, F3, 17, 17) (dual of [(597872, 17), 10163669, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3155, 4782977, F3, 17) (dual of [4782977, 4782822, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3155, 4782983, F3, 17) (dual of [4782983, 4782828, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- 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(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(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3155, 4782983, F3, 17) (dual of [4782983, 4782828, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3155, 4782977, F3, 17) (dual of [4782977, 4782822, 18]-code), using
- net defined by OOA [i] based on linear OOA(3155, 597872, F3, 17, 17) (dual of [(597872, 17), 10163669, 18]-NRT-code), using
- digital (1, 9, 7)-net over F3, using
(147, 147+17, 1594340)-Net over F3 — Digital
Digital (147, 164, 1594340)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3164, 1594340, F3, 3, 17) (dual of [(1594340, 3), 4782856, 18]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3161, 1594339, F3, 3, 17) (dual of [(1594339, 3), 4782856, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3161, 4783017, F3, 17) (dual of [4783017, 4782856, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- 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(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]
- 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(16) ⊂ Ce(12) [i] based on
- OOA 3-folding [i] based on linear OA(3161, 4783017, F3, 17) (dual of [4783017, 4782856, 18]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3161, 1594339, F3, 3, 17) (dual of [(1594339, 3), 4782856, 18]-NRT-code), using
(147, 147+17, large)-Net in Base 3 — Upper bound on s
There is no (147, 164, large)-net in base 3, because
- 15 times m-reduction [i] would yield (147, 149, large)-net in base 3, but