Best Known (69, 95, s)-Nets in Base 9
(69, 95, 740)-Net over F9 — Constructive and digital
Digital (69, 95, 740)-net over F9, using
- 11 times m-reduction [i] based on digital (69, 106, 740)-net over F9, 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
(69, 95, 6572)-Net over F9 — Digital
Digital (69, 95, 6572)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(995, 6572, F9, 26) (dual of [6572, 6477, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(23) ⊂ Ce(22) [i] based on
- linear OA(993, 6561, F9, 26) (dual of [6561, 6468, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(985, 6561, F9, 24) (dual of [6561, 6476, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(981, 6561, F9, 23) (dual of [6561, 6480, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(91, 10, F9, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(25) ⊂ Ce(23) ⊂ Ce(22) [i] based on
(69, 95, 6662333)-Net in Base 9 — Upper bound on s
There is no (69, 95, 6662334)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 4 498204 459328 716459 767003 342301 508309 470788 817048 284301 027830 819354 431853 203243 064028 213425 > 995 [i]