Best Known (50, 50+18, s)-Nets in Base 9
(50, 50+18, 740)-Net over F9 — Constructive and digital
Digital (50, 68, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 34, 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
(50, 50+18, 6576)-Net over F9 — Digital
Digital (50, 68, 6576)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(968, 6576, F9, 18) (dual of [6576, 6508, 19]-code), using
- 1 times truncation [i] based on linear OA(969, 6577, F9, 19) (dual of [6577, 6508, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(965, 6561, F9, 19) (dual of [6561, 6496, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(953, 6561, F9, 15) (dual of [6561, 6508, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(94, 16, F9, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,9)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(969, 6577, F9, 19) (dual of [6577, 6508, 20]-code), using
(50, 50+18, large)-Net in Base 9 — Upper bound on s
There is no (50, 68, large)-net in base 9, because
- 16 times m-reduction [i] would yield (50, 52, large)-net in base 9, but