Best Known (182−34, 182, s)-Nets in Base 3
(182−34, 182, 695)-Net over F3 — Constructive and digital
Digital (148, 182, 695)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 18, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (130, 164, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 41, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 41, 172)-net over F81, using
- digital (1, 18, 7)-net over F3, using
(182−34, 182, 3291)-Net over F3 — Digital
Digital (148, 182, 3291)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3182, 3291, F3, 2, 34) (dual of [(3291, 2), 6400, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3182, 6582, F3, 34) (dual of [6582, 6400, 35]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3181, 6581, F3, 34) (dual of [6581, 6400, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(34, 20, F3, 2) (dual of [20, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3181, 6581, F3, 34) (dual of [6581, 6400, 35]-code), using
- OOA 2-folding [i] based on linear OA(3182, 6582, F3, 34) (dual of [6582, 6400, 35]-code), using
(182−34, 182, 460154)-Net in Base 3 — Upper bound on s
There is no (148, 182, 460155)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 685 609158 055428 848293 990470 429577 785926 857783 838558 543432 885546 289567 364533 370577 522007 > 3182 [i]