Best Known (20, 20+10, s)-Nets in Base 9
(20, 20+10, 328)-Net over F9 — Constructive and digital
Digital (20, 30, 328)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 10, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 5, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 5, 82)-net over F81, using
- digital (10, 20, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 10, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- trace code for nets [i] based on digital (0, 10, 82)-net over F81, using
- digital (5, 10, 164)-net over F9, using
(20, 20+10, 867)-Net over F9 — Digital
Digital (20, 30, 867)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(930, 867, F9, 10) (dual of [867, 837, 11]-code), using
- 133 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 10 times 0, 1, 33 times 0, 1, 83 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]
- 133 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 10 times 0, 1, 33 times 0, 1, 83 times 0) [i] based on linear OA(925, 729, F9, 10) (dual of [729, 704, 11]-code), using
(20, 20+10, 173059)-Net in Base 9 — Upper bound on s
There is no (20, 30, 173060)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 42392 118704 679693 340442 573217 > 930 [i]