Best Known (141−42, 141, s)-Nets in Base 9
(141−42, 141, 770)-Net over F9 — Constructive and digital
Digital (99, 141, 770)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (4, 25, 30)-net over F9, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 4 and N(F) ≥ 30, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- digital (74, 116, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 58, 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, 58, 370)-net over F81, using
- digital (4, 25, 30)-net over F9, using
(141−42, 141, 3880)-Net over F9 — Digital
Digital (99, 141, 3880)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9141, 3880, F9, 42) (dual of [3880, 3739, 43]-code), using
- 3738 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 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, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 36 times 0, 1, 39 times 0, 1, 40 times 0, 1, 43 times 0, 1, 45 times 0, 1, 48 times 0, 1, 51 times 0, 1, 54 times 0, 1, 57 times 0, 1, 60 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 74 times 0, 1, 79 times 0, 1, 84 times 0, 1, 88 times 0, 1, 93 times 0, 1, 98 times 0, 1, 104 times 0, 1, 110 times 0, 1, 116 times 0, 1, 122 times 0, 1, 129 times 0, 1, 136 times 0, 1, 144 times 0, 1, 152 times 0, 1, 161 times 0, 1, 169 times 0, 1, 179 times 0, 1, 189 times 0, 1, 200 times 0) [i] based on linear OA(942, 43, F9, 42) (dual of [43, 1, 43]-code or 43-arc in PG(41,9)), using
- dual of repetition code with length 43 [i]
- 3738 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 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, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 36 times 0, 1, 39 times 0, 1, 40 times 0, 1, 43 times 0, 1, 45 times 0, 1, 48 times 0, 1, 51 times 0, 1, 54 times 0, 1, 57 times 0, 1, 60 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 74 times 0, 1, 79 times 0, 1, 84 times 0, 1, 88 times 0, 1, 93 times 0, 1, 98 times 0, 1, 104 times 0, 1, 110 times 0, 1, 116 times 0, 1, 122 times 0, 1, 129 times 0, 1, 136 times 0, 1, 144 times 0, 1, 152 times 0, 1, 161 times 0, 1, 169 times 0, 1, 179 times 0, 1, 189 times 0, 1, 200 times 0) [i] based on linear OA(942, 43, F9, 42) (dual of [43, 1, 43]-code or 43-arc in PG(41,9)), using
(141−42, 141, 2769857)-Net in Base 9 — Upper bound on s
There is no (99, 141, 2769858)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 353 341778 187548 287862 537851 932223 137687 605624 770730 921015 453930 420343 951143 446444 731907 654393 588413 569916 837797 560947 196356 583100 916945 > 9141 [i]