Best Known (27−10, 27, s)-Nets in Base 9
(27−10, 27, 232)-Net over F9 — Constructive and digital
Digital (17, 27, 232)-net over F9, using
- 3 times m-reduction [i] based on digital (17, 30, 232)-net over F9, using
- trace code for nets [i] based on digital (2, 15, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 15, 116)-net over F81, using
(27−10, 27, 590)-Net over F9 — Digital
Digital (17, 27, 590)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(927, 590, F9, 10) (dual of [590, 563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(927, 728, F9, 10) (dual of [728, 701, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(927, 728, F9, 10) (dual of [728, 701, 11]-code), using
(27−10, 27, 46305)-Net in Base 9 — Upper bound on s
There is no (17, 27, 46306)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 58 153802 453854 533620 966097 > 927 [i]