Best Known (208, 208+38, s)-Nets in Base 3
(208, 208+38, 1500)-Net over F3 — Constructive and digital
Digital (208, 246, 1500)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (11, 30, 20)-net over F3, using
- net from sequence [i] based on digital (11, 19)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 9, N(F) = 19, and 1 place with degree 3 [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (11, 19)-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 (11, 30, 20)-net over F3, using
(208, 208+38, 12577)-Net over F3 — Digital
Digital (208, 246, 12577)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3246, 12577, F3, 38) (dual of [12577, 12331, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 19748, F3, 38) (dual of [19748, 19502, 39]-code), using
- 5 times code embedding in larger space [i] based on linear OA(3241, 19743, F3, 38) (dual of [19743, 19502, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(30) [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(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(315, 60, F3, 6) (dual of [60, 45, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(37) ⊂ Ce(30) [i] based on
- 5 times code embedding in larger space [i] based on linear OA(3241, 19743, F3, 38) (dual of [19743, 19502, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 19748, F3, 38) (dual of [19748, 19502, 39]-code), using
(208, 208+38, 5965527)-Net in Base 3 — Upper bound on s
There is no (208, 246, 5965528)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2354 126339 958010 653318 912521 313160 727710 730011 652373 971020 836799 124027 228566 775632 132887 339514 858973 052327 912763 404513 > 3246 [i]