Best Known (235−38, 235, s)-Nets in Base 3
(235−38, 235, 1484)-Net over F3 — Constructive and digital
Digital (197, 235, 1484)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 19, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- 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
- digital (0, 19, 4)-net over F3, using
(235−38, 235, 9859)-Net over F3 — Digital
Digital (197, 235, 9859)-net over F3, using
- 31 times duplication [i] based on digital (196, 234, 9859)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3234, 9859, F3, 2, 38) (dual of [(9859, 2), 19484, 39]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3232, 9858, F3, 2, 38) (dual of [(9858, 2), 19484, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3232, 19716, F3, 38) (dual of [19716, 19484, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
- linear OA(3226, 19683, F3, 38) (dual of [19683, 19457, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3199, 19683, F3, 34) (dual of [19683, 19484, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(37) ⊂ Ce(33) [i] based on
- OOA 2-folding [i] based on linear OA(3232, 19716, F3, 38) (dual of [19716, 19484, 39]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3232, 9858, F3, 2, 38) (dual of [(9858, 2), 19484, 39]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3234, 9859, F3, 2, 38) (dual of [(9859, 2), 19484, 39]-NRT-code), using
(235−38, 235, 3158053)-Net in Base 3 — Upper bound on s
There is no (197, 235, 3158054)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 13289 086198 335309 388656 609703 003934 312252 318895 189687 813881 089004 604504 309063 421664 126267 374664 308910 088708 015041 > 3235 [i]