Best Known (128−36, 128, s)-Nets in Base 9
(128−36, 128, 774)-Net over F9 — Constructive and digital
Digital (92, 128, 774)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 24, 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 (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 (6, 24, 34)-net over F9, using
(128−36, 128, 6185)-Net over F9 — Digital
Digital (92, 128, 6185)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9128, 6185, F9, 36) (dual of [6185, 6057, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(9128, 6561, F9, 36) (dual of [6561, 6433, 37]-code), using
- 1 times truncation [i] based on linear OA(9129, 6562, F9, 37) (dual of [6562, 6433, 38]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(9129, 6562, F9, 37) (dual of [6562, 6433, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(9128, 6561, F9, 36) (dual of [6561, 6433, 37]-code), using
(128−36, 128, 5764528)-Net in Base 9 — Upper bound on s
There is no (92, 128, 5764529)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 139 008780 756295 412351 128419 105206 964704 142304 154328 156895 133067 320577 623906 592421 676907 794813 592239 297710 511022 969577 302993 > 9128 [i]