Best Known (19, 29, s)-Nets in Base 9
(19, 29, 300)-Net over F9 — Constructive and digital
Digital (19, 29, 300)-net over F9, using
- 1 times m-reduction [i] based on digital (19, 30, 300)-net over F9, using
- trace code for nets [i] based on digital (4, 15, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 15, 150)-net over F81, using
(19, 29, 782)-Net over F9 — Digital
Digital (19, 29, 782)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(929, 782, F9, 10) (dual of [782, 753, 11]-code), using
- 49 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 10 times 0, 1, 33 times 0) [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]
- 49 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 10 times 0, 1, 33 times 0) [i] based on linear OA(925, 729, F9, 10) (dual of [729, 704, 11]-code), using
(19, 29, 111517)-Net in Base 9 — Upper bound on s
There is no (19, 29, 111518)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 4710 257632 529487 766764 026673 > 929 [i]