Best Known (38, 56, s)-Nets in Base 9
(38, 56, 364)-Net over F9 — Constructive and digital
Digital (38, 56, 364)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (9, 18, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 9, 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, 9, 82)-net over F81, using
- digital (20, 38, 200)-net over F9, using
- trace code for nets [i] based on digital (1, 19, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 19, 100)-net over F81, using
- digital (9, 18, 164)-net over F9, using
(38, 56, 1257)-Net over F9 — Digital
Digital (38, 56, 1257)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(956, 1257, F9, 18) (dual of [1257, 1201, 19]-code), using
- 1200 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 8 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 15 times 0, 1, 17 times 0, 1, 20 times 0, 1, 23 times 0, 1, 26 times 0, 1, 30 times 0, 1, 35 times 0, 1, 39 times 0, 1, 45 times 0, 1, 52 times 0, 1, 59 times 0, 1, 68 times 0, 1, 77 times 0, 1, 89 times 0, 1, 100 times 0, 1, 115 times 0, 1, 131 times 0, 1, 150 times 0) [i] based on linear OA(918, 19, F9, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,9)), using
- dual of repetition code with length 19 [i]
- 1200 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 8 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 15 times 0, 1, 17 times 0, 1, 20 times 0, 1, 23 times 0, 1, 26 times 0, 1, 30 times 0, 1, 35 times 0, 1, 39 times 0, 1, 45 times 0, 1, 52 times 0, 1, 59 times 0, 1, 68 times 0, 1, 77 times 0, 1, 89 times 0, 1, 100 times 0, 1, 115 times 0, 1, 131 times 0, 1, 150 times 0) [i] based on linear OA(918, 19, F9, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,9)), using
(38, 56, 448916)-Net in Base 9 — Upper bound on s
There is no (38, 56, 448917)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 273896 157761 320751 673563 052914 326214 206620 675943 532777 > 956 [i]