Best Known (173, 173+34, s)-Nets in Base 3
(173, 173+34, 1480)-Net over F3 — Constructive and digital
Digital (173, 207, 1480)-net over F3, using
- t-expansion [i] based on digital (172, 207, 1480)-net over F3, using
- 1 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
- 1 times m-reduction [i] based on digital (172, 208, 1480)-net over F3, using
(173, 173+34, 8845)-Net over F3 — Digital
Digital (173, 207, 8845)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3207, 8845, F3, 2, 34) (dual of [(8845, 2), 17483, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3207, 9859, F3, 2, 34) (dual of [(9859, 2), 19511, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3207, 19718, F3, 34) (dual of [19718, 19511, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- linear OA(3199, 19683, F3, 34) (dual of [19683, 19484, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(38, 35, F3, 4) (dual of [35, 27, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- OOA 2-folding [i] based on linear OA(3207, 19718, F3, 34) (dual of [19718, 19511, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(3207, 9859, F3, 2, 34) (dual of [(9859, 2), 19511, 35]-NRT-code), using
(173, 173+34, 2315074)-Net in Base 3 — Upper bound on s
There is no (173, 207, 2315075)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 580 898343 916581 578057 771186 726365 471835 899407 651670 931701 971670 918242 239204 174020 395371 248705 367271 > 3207 [i]