Best Known (175, 175+34, s)-Nets in Base 3
(175, 175+34, 1480)-Net over F3 — Constructive and digital
Digital (175, 209, 1480)-net over F3, using
- 3 times m-reduction [i] based on digital (175, 212, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 53, 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, 53, 370)-net over F81, using
(175, 175+34, 9497)-Net over F3 — Digital
Digital (175, 209, 9497)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3209, 9497, F3, 2, 34) (dual of [(9497, 2), 18785, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3209, 9861, F3, 2, 34) (dual of [(9861, 2), 19513, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3209, 19722, F3, 34) (dual of [19722, 19513, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(27) [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(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(310, 39, F3, 5) (dual of [39, 29, 6]-code), using
- construction X applied to Ce(33) ⊂ Ce(27) [i] based on
- OOA 2-folding [i] based on linear OA(3209, 19722, F3, 34) (dual of [19722, 19513, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(3209, 9861, F3, 2, 34) (dual of [(9861, 2), 19513, 35]-NRT-code), using
(175, 175+34, 2634494)-Net in Base 3 — Upper bound on s
There is no (175, 209, 2634495)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 5228 090398 825630 074019 880746 214662 954619 759434 711552 655133 718277 082259 244853 358466 288822 760684 185055 > 3209 [i]