Best Known (134−34, 134, s)-Nets in Base 9
(134−34, 134, 904)-Net over F9 — Constructive and digital
Digital (100, 134, 904)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (17, 34, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 17, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 17, 82)-net over F81, using
- digital (66, 100, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 50, 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, 50, 370)-net over F81, using
- digital (17, 34, 164)-net over F9, using
(134−34, 134, 13126)-Net over F9 — Digital
Digital (100, 134, 13126)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9134, 13126, F9, 34) (dual of [13126, 12992, 35]-code), using
- trace code [i] based on linear OA(8167, 6563, F81, 34) (dual of [6563, 6496, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- linear OA(8167, 6561, F81, 34) (dual of [6561, 6494, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8165, 6561, F81, 33) (dual of [6561, 6496, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- trace code [i] based on linear OA(8167, 6563, F81, 34) (dual of [6563, 6496, 35]-code), using
(134−34, 134, large)-Net in Base 9 — Upper bound on s
There is no (100, 134, large)-net in base 9, because
- 32 times m-reduction [i] would yield (100, 102, large)-net in base 9, but