Best Known (162, 196, s)-Nets in Base 3
(162, 196, 896)-Net over F3 — Constructive and digital
Digital (162, 196, 896)-net over F3, using
- t-expansion [i] based on digital (160, 196, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 49, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 49, 224)-net over F81, using
(162, 196, 5137)-Net over F3 — Digital
Digital (162, 196, 5137)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3196, 5137, F3, 34) (dual of [5137, 4941, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, 6620, F3, 34) (dual of [6620, 6424, 35]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3193, 6617, F3, 34) (dual of [6617, 6424, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3137, 6561, F3, 26) (dual of [6561, 6424, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(316, 56, F3, 7) (dual of [56, 40, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(3193, 6617, F3, 34) (dual of [6617, 6424, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, 6620, F3, 34) (dual of [6620, 6424, 35]-code), using
(162, 196, 1137198)-Net in Base 3 — Upper bound on s
There is no (162, 196, 1137199)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3279 204545 023073 331433 037482 246187 103330 216760 337995 598885 122640 325042 424184 460464 253499 475007 > 3196 [i]