Best Known (211, 249, s)-Nets in Base 3
(211, 249, 1504)-Net over F3 — Constructive and digital
Digital (211, 249, 1504)-net over F3, using
- 31 times duplication [i] based on digital (210, 248, 1504)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (13, 32, 24)-net over F3, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 13 and N(F) ≥ 24, using
- net from sequence [i] based on digital (13, 23)-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 (13, 32, 24)-net over F3, using
- (u, u+v)-construction [i] based on
(211, 249, 13786)-Net over F3 — Digital
Digital (211, 249, 13786)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3249, 13786, F3, 38) (dual of [13786, 13537, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(3249, 19760, F3, 38) (dual of [19760, 19511, 39]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3247, 19758, F3, 38) (dual of [19758, 19511, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(28) [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(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(321, 75, F3, 8) (dual of [75, 54, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
- construction X applied to Ce(37) ⊂ Ce(28) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3247, 19758, F3, 38) (dual of [19758, 19511, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(3249, 19760, F3, 38) (dual of [19760, 19511, 39]-code), using
(211, 249, 7095515)-Net in Base 3 — Upper bound on s
There is no (211, 249, 7095516)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 63561 260443 066517 739802 404963 256517 360629 093310 598178 593031 370959 527188 941580 914251 250619 766315 572815 380656 051278 504465 > 3249 [i]