Best Known (9, 15, s)-Nets in Base 9
(9, 15, 200)-Net over F9 — Constructive and digital
Digital (9, 15, 200)-net over F9, using
- 1 times m-reduction [i] based on digital (9, 16, 200)-net over F9, using
- trace code for nets [i] based on digital (1, 8, 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, 8, 100)-net over F81, using
(9, 15, 367)-Net over F9 — Digital
Digital (9, 15, 367)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(915, 367, F9, 6) (dual of [367, 352, 7]-code), using
- construction X applied to C([40,45]) ⊂ C([41,45]) [i] based on
- linear OA(915, 364, F9, 6) (dual of [364, 349, 7]-code), using the BCH-code C(I) with length 364 | 93−1, defining interval I = {40,41,…,45}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(912, 364, F9, 5) (dual of [364, 352, 6]-code), using the BCH-code C(I) with length 364 | 93−1, defining interval I = {41,42,43,44,45}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to C([40,45]) ⊂ C([41,45]) [i] based on
(9, 15, 13411)-Net in Base 9 — Upper bound on s
There is no (9, 15, 13412)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 205 936299 384033 > 915 [i]