Best Known (180, 215, s)-Nets in Base 3
(180, 215, 1480)-Net over F3 — Constructive and digital
Digital (180, 215, 1480)-net over F3, using
- t-expansion [i] based on digital (178, 215, 1480)-net over F3, using
- 1 times m-reduction [i] based on digital (178, 216, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 54, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 54, 370)-net over F81, using
- 1 times m-reduction [i] based on digital (178, 216, 1480)-net over F3, using
(180, 215, 9556)-Net over F3 — Digital
Digital (180, 215, 9556)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3215, 9556, F3, 2, 35) (dual of [(9556, 2), 18897, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3215, 9858, F3, 2, 35) (dual of [(9858, 2), 19501, 36]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3214, 9858, F3, 2, 35) (dual of [(9858, 2), 19502, 36]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3214, 19716, F3, 35) (dual of [19716, 19502, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- linear OA(3208, 19683, F3, 35) (dual of [19683, 19475, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(36, 33, F3, 3) (dual of [33, 27, 4]-code or 33-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on 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(34) ⊂ Ce(30) [i] based on
- OOA 2-folding [i] based on linear OA(3214, 19716, F3, 35) (dual of [19716, 19502, 36]-code), using
- 31 times duplication [i] based on linear OOA(3214, 9858, F3, 2, 35) (dual of [(9858, 2), 19502, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3215, 9858, F3, 2, 35) (dual of [(9858, 2), 19501, 36]-NRT-code), using
(180, 215, 3639383)-Net in Base 3 — Upper bound on s
There is no (180, 215, 3639384)-net in base 3, because
- 1 times m-reduction [i] would yield (180, 214, 3639384)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 270424 522163 000835 723498 313825 492790 127755 835665 505130 006316 722772 837918 745752 892783 755182 631978 315697 > 3214 [i]