Best Known (94, 134, s)-Nets in Base 9
(94, 134, 760)-Net over F9 — Constructive and digital
Digital (94, 134, 760)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 22, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (72, 112, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 56, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 56, 370)-net over F81, using
- digital (2, 22, 20)-net over F9, using
(94, 134, 3676)-Net over F9 — Digital
Digital (94, 134, 3676)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9134, 3676, F9, 40) (dual of [3676, 3542, 41]-code), using
- 3541 step Varšamov–Edel lengthening with (ri) = (6, 3, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 6 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 39 times 0, 1, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 50 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 79 times 0, 1, 84 times 0, 1, 89 times 0, 1, 94 times 0, 1, 100 times 0, 1, 106 times 0, 1, 112 times 0, 1, 118 times 0, 1, 126 times 0, 1, 133 times 0, 1, 141 times 0, 1, 149 times 0, 1, 158 times 0, 1, 167 times 0, 1, 177 times 0, 1, 187 times 0, 1, 199 times 0) [i] based on linear OA(940, 41, F9, 40) (dual of [41, 1, 41]-code or 41-arc in PG(39,9)), using
- dual of repetition code with length 41 [i]
- 3541 step Varšamov–Edel lengthening with (ri) = (6, 3, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 6 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 39 times 0, 1, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 50 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 79 times 0, 1, 84 times 0, 1, 89 times 0, 1, 94 times 0, 1, 100 times 0, 1, 106 times 0, 1, 112 times 0, 1, 118 times 0, 1, 126 times 0, 1, 133 times 0, 1, 141 times 0, 1, 149 times 0, 1, 158 times 0, 1, 167 times 0, 1, 177 times 0, 1, 187 times 0, 1, 199 times 0) [i] based on linear OA(940, 41, F9, 40) (dual of [41, 1, 41]-code or 41-arc in PG(39,9)), using
(94, 134, 2568260)-Net in Base 9 — Upper bound on s
There is no (94, 134, 2568261)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 73 875229 810197 226704 967692 185468 926486 646770 615316 431815 527990 870446 938773 983038 943272 605163 782283 569425 651847 830790 206859 959201 > 9134 [i]