Best Known (205−32, 205, s)-Nets in Base 3
(205−32, 205, 1480)-Net over F3 — Constructive and digital
Digital (173, 205, 1480)-net over F3, using
- t-expansion [i] based on digital (172, 205, 1480)-net over F3, using
- 3 times m-reduction [i] based on digital (172, 208, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 52, 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, 52, 370)-net over F81, using
- 3 times m-reduction [i] based on digital (172, 208, 1480)-net over F3, using
(205−32, 205, 10544)-Net over F3 — Digital
Digital (173, 205, 10544)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3205, 10544, F3, 32) (dual of [10544, 10339, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3205, 19743, F3, 32) (dual of [19743, 19538, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(24) [i] based on
- linear OA(3190, 19683, F3, 32) (dual of [19683, 19493, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(31) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(3205, 19743, F3, 32) (dual of [19743, 19538, 33]-code), using
(205−32, 205, 4411875)-Net in Base 3 — Upper bound on s
There is no (173, 205, 4411876)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 64 544243 079465 945264 505603 814915 157119 966858 754741 717436 334047 057304 255666 715220 895766 654708 974721 > 3205 [i]