Best Known (161−34, 161, s)-Nets in Base 3
(161−34, 161, 640)-Net over F3 — Constructive and digital
Digital (127, 161, 640)-net over F3, using
- 31 times duplication [i] based on digital (126, 160, 640)-net over F3, using
- t-expansion [i] based on digital (125, 160, 640)-net over F3, using
- trace code for nets [i] based on digital (5, 40, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- trace code for nets [i] based on digital (5, 40, 160)-net over F81, using
- t-expansion [i] based on digital (125, 160, 640)-net over F3, using
(161−34, 161, 1525)-Net over F3 — Digital
Digital (127, 161, 1525)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3161, 1525, F3, 34) (dual of [1525, 1364, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3161, 2208, F3, 34) (dual of [2208, 2047, 35]-code), using
- construction XX applied to Ce(33) ⊂ Ce(30) ⊂ Ce(28) [i] based on
- linear OA(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3141, 2187, F3, 31) (dual of [2187, 2046, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3134, 2187, F3, 29) (dual of [2187, 2053, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(34, 19, F3, 2) (dual of [19, 15, 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
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(33) ⊂ Ce(30) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(3161, 2208, F3, 34) (dual of [2208, 2047, 35]-code), using
(161−34, 161, 118433)-Net in Base 3 — Upper bound on s
There is no (127, 161, 118434)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 65549 385115 356508 855721 561717 142535 647308 637692 334130 761473 820987 132343 802277 > 3161 [i]