Best Known (142−36, 142, s)-Nets in Base 9
(142−36, 142, 940)-Net over F9 — Constructive and digital
Digital (106, 142, 940)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (20, 38, 200)-net over F9, using
- trace code for nets [i] based on digital (1, 19, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 19, 100)-net over F81, using
- digital (68, 104, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 52, 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, 52, 370)-net over F81, using
- digital (20, 38, 200)-net over F9, using
(142−36, 142, 13126)-Net over F9 — Digital
Digital (106, 142, 13126)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9142, 13126, F9, 36) (dual of [13126, 12984, 37]-code), using
- trace code [i] based on linear OA(8171, 6563, F81, 36) (dual of [6563, 6492, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- linear OA(8171, 6561, F81, 36) (dual of [6561, 6490, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8169, 6561, F81, 35) (dual of [6561, 6492, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(35) ⊂ Ce(34) [i] based on
- trace code [i] based on linear OA(8171, 6563, F81, 36) (dual of [6563, 6492, 37]-code), using
(142−36, 142, large)-Net in Base 9 — Upper bound on s
There is no (106, 142, large)-net in base 9, because
- 34 times m-reduction [i] would yield (106, 108, large)-net in base 9, but