Best Known (160, 160+32, s)-Nets in Base 3
(160, 160+32, 1480)-Net over F3 — Constructive and digital
Digital (160, 192, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 48, 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
(160, 160+32, 7771)-Net over F3 — Digital
Digital (160, 192, 7771)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3192, 7771, F3, 2, 32) (dual of [(7771, 2), 15350, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3192, 9847, F3, 2, 32) (dual of [(9847, 2), 19502, 33]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3190, 9846, F3, 2, 32) (dual of [(9846, 2), 19502, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3190, 19692, F3, 32) (dual of [19692, 19502, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [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(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(30, 9, F3, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- OOA 2-folding [i] based on linear OA(3190, 19692, F3, 32) (dual of [19692, 19502, 33]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3190, 9846, F3, 2, 32) (dual of [(9846, 2), 19502, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3192, 9847, F3, 2, 32) (dual of [(9847, 2), 19502, 33]-NRT-code), using
(160, 160+32, 1807007)-Net in Base 3 — Upper bound on s
There is no (160, 192, 1807008)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 40 483788 274154 406776 780387 816585 760586 503766 398610 724827 220710 750110 242324 175377 183454 672897 > 3192 [i]