Best Known (38−14, 38, s)-Nets in Base 9
(38−14, 38, 320)-Net over F9 — Constructive and digital
Digital (24, 38, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 19, 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
(38−14, 38, 573)-Net over F9 — Digital
Digital (24, 38, 573)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(938, 573, F9, 14) (dual of [573, 535, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(938, 736, F9, 14) (dual of [736, 698, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(937, 729, F9, 14) (dual of [729, 692, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(931, 729, F9, 12) (dual of [729, 698, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(91, 7, F9, 1) (dual of [7, 6, 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(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(938, 736, F9, 14) (dual of [736, 698, 15]-code), using
(38−14, 38, 63969)-Net in Base 9 — Upper bound on s
There is no (24, 38, 63970)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1 824811 338617 655342 174455 051706 047793 > 938 [i]