Best Known (85, 85+32, s)-Nets in Base 9
(85, 85+32, 772)-Net over F9 — Constructive and digital
Digital (85, 117, 772)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 21, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (64, 96, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 48, 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, 48, 370)-net over F81, using
- digital (5, 21, 32)-net over F9, using
(85, 85+32, 6581)-Net over F9 — Digital
Digital (85, 117, 6581)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9117, 6581, F9, 32) (dual of [6581, 6464, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- linear OA(9113, 6561, F9, 32) (dual of [6561, 6448, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(997, 6561, F9, 28) (dual of [6561, 6464, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(94, 20, F9, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,9)), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
(85, 85+32, 8078794)-Net in Base 9 — Upper bound on s
There is no (85, 117, 8078795)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 4429 694519 806134 002521 736661 647842 213724 166395 018050 911928 912044 194258 672912 194951 152358 913539 889136 641776 116097 > 9117 [i]