Best Known (162, 194, s)-Nets in Base 3
(162, 194, 1480)-Net over F3 — Constructive and digital
Digital (162, 194, 1480)-net over F3, using
- 32 times duplication [i] based on digital (160, 192, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 48, 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, 48, 370)-net over F81, using
(162, 194, 8385)-Net over F3 — Digital
Digital (162, 194, 8385)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3194, 8385, F3, 2, 32) (dual of [(8385, 2), 16576, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3194, 9852, F3, 2, 32) (dual of [(9852, 2), 19510, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3194, 19704, F3, 32) (dual of [19704, 19510, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3194, 19705, F3, 32) (dual of [19705, 19511, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- linear OA(3190, 19683, F3, 32) (dual of [19683, 19493, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3172, 19683, F3, 29) (dual of [19683, 19511, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(34, 22, F3, 2) (dual of [22, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(3194, 19705, F3, 32) (dual of [19705, 19511, 33]-code), using
- OOA 2-folding [i] based on linear OA(3194, 19704, F3, 32) (dual of [19704, 19510, 33]-code), using
- discarding factors / shortening the dual code based on linear OOA(3194, 9852, F3, 2, 32) (dual of [(9852, 2), 19510, 33]-NRT-code), using
(162, 194, 2073006)-Net in Base 3 — Upper bound on s
There is no (162, 194, 2073007)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 364 354879 418067 897903 477047 326200 859335 129613 189842 578550 065319 012650 161877 955212 162735 458785 > 3194 [i]