Best Known (95, 133, s)-Nets in Base 9
(95, 133, 774)-Net over F9 — Constructive and digital
Digital (95, 133, 774)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 25, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- digital (70, 108, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 54, 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, 54, 370)-net over F81, using
- digital (6, 25, 34)-net over F9, using
(95, 133, 5609)-Net over F9 — Digital
Digital (95, 133, 5609)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9133, 5609, F9, 38) (dual of [5609, 5476, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(9133, 6561, F9, 38) (dual of [6561, 6428, 39]-code), using
- an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- discarding factors / shortening the dual code based on linear OA(9133, 6561, F9, 38) (dual of [6561, 6428, 39]-code), using
(95, 133, 4740476)-Net in Base 9 — Upper bound on s
There is no (95, 133, 4740477)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 8 208310 261907 264207 411340 289144 576680 105698 400953 619995 018564 980152 644429 022404 240148 179787 834998 329188 158324 398940 798991 687801 > 9133 [i]