Best Known (39−14, 39, s)-Nets in Base 9
(39−14, 39, 320)-Net over F9 — Constructive and digital
Digital (25, 39, 320)-net over F9, using
- 1 times m-reduction [i] based on digital (25, 40, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 20, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- trace code for nets [i] based on digital (5, 20, 160)-net over F81, using
(39−14, 39, 689)-Net over F9 — Digital
Digital (25, 39, 689)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(939, 689, F9, 14) (dual of [689, 650, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(939, 728, F9, 14) (dual of [728, 689, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(939, 728, F9, 14) (dual of [728, 689, 15]-code), using
(39−14, 39, 87559)-Net in Base 9 — Upper bound on s
There is no (25, 39, 87560)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 16 423820 007847 680221 698349 785258 131137 > 939 [i]