Best Known (16, 26, s)-Nets in Base 9
(16, 26, 232)-Net over F9 — Constructive and digital
Digital (16, 26, 232)-net over F9, using
- 2 times m-reduction [i] based on digital (16, 28, 232)-net over F9, using
- trace code for nets [i] based on digital (2, 14, 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, 14, 116)-net over F81, using
(16, 26, 448)-Net over F9 — Digital
Digital (16, 26, 448)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(926, 448, F9, 10) (dual of [448, 422, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(926, 733, F9, 10) (dual of [733, 707, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(925, 729, F9, 10) (dual of [729, 704, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(922, 729, F9, 8) (dual of [729, 707, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(91, 4, F9, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(926, 733, F9, 10) (dual of [733, 707, 11]-code), using
(16, 26, 29837)-Net in Base 9 — Upper bound on s
There is no (16, 26, 29838)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 6 461126 710277 848328 690865 > 926 [i]