Best Known (203, 203+38, s)-Nets in Base 3
(203, 203+38, 1494)-Net over F3 — Constructive and digital
Digital (203, 241, 1494)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (6, 25, 14)-net over F3, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 6 and N(F) ≥ 14, using
- net from sequence [i] based on digital (6, 13)-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 (6, 25, 14)-net over F3, using
(203, 203+38, 10792)-Net over F3 — Digital
Digital (203, 241, 10792)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3241, 10792, F3, 38) (dual of [10792, 10551, 39]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(3241, 19743, F3, 38) (dual of [19743, 19502, 39]-code), using
(203, 203+38, 4467763)-Net in Base 3 — Upper bound on s
There is no (203, 241, 4467764)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 9 687767 946087 589235 109788 485847 777692 050260 542913 999790 100291 919969 449050 082587 906077 058125 529771 951773 216554 594673 > 3241 [i]