Best Known (160, 160+22, s)-Nets in Base 3
(160, 160+22, 48321)-Net over F3 — Constructive and digital
Digital (160, 182, 48321)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 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 (148, 170, 48314)-net over F3, using
- net defined by OOA [i] based on linear OOA(3170, 48314, F3, 22, 22) (dual of [(48314, 22), 1062738, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3170, 531454, F3, 22) (dual of [531454, 531284, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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(21) ⊂ Ce(19) [i] based on
- OA 11-folding and stacking [i] based on linear OA(3170, 531454, F3, 22) (dual of [531454, 531284, 23]-code), using
- net defined by OOA [i] based on linear OOA(3170, 48314, F3, 22, 22) (dual of [(48314, 22), 1062738, 23]-NRT-code), using
- digital (1, 12, 7)-net over F3, using
(160, 160+22, 177167)-Net over F3 — Digital
Digital (160, 182, 177167)-net over F3, using
- 31 times duplication [i] based on digital (159, 181, 177167)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3181, 177167, F3, 3, 22) (dual of [(177167, 3), 531320, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3181, 531501, F3, 22) (dual of [531501, 531320, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3180, 531500, F3, 22) (dual of [531500, 531320, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(311, 59, F3, 5) (dual of [59, 48, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3180, 531500, F3, 22) (dual of [531500, 531320, 23]-code), using
- OOA 3-folding [i] based on linear OA(3181, 531501, F3, 22) (dual of [531501, 531320, 23]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3181, 177167, F3, 3, 22) (dual of [(177167, 3), 531320, 23]-NRT-code), using
(160, 160+22, large)-Net in Base 3 — Upper bound on s
There is no (160, 182, large)-net in base 3, because
- 20 times m-reduction [i] would yield (160, 162, large)-net in base 3, but