Best Known (112, 112+34, s)-Nets in Base 5
(112, 112+34, 504)-Net over F5 — Constructive and digital
Digital (112, 146, 504)-net over F5, using
- 2 times m-reduction [i] based on digital (112, 148, 504)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (38, 56, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 28, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 28, 126)-net over F25, using
- digital (56, 92, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 46, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25 (see above)
- trace code for nets [i] based on digital (10, 46, 126)-net over F25, using
- digital (38, 56, 252)-net over F5, using
- (u, u+v)-construction [i] based on
(112, 112+34, 4088)-Net over F5 — Digital
Digital (112, 146, 4088)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5146, 4088, F5, 34) (dual of [4088, 3942, 35]-code), using
- 3941 step Varšamov–Edel lengthening with (ri) = (8, 4, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 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, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 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, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 38 times 0, 1, 41 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 50 times 0, 1, 53 times 0, 1, 55 times 0, 1, 58 times 0, 1, 61 times 0, 1, 65 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 79 times 0, 1, 82 times 0, 1, 87 times 0, 1, 91 times 0, 1, 96 times 0, 1, 101 times 0, 1, 106 times 0, 1, 111 times 0, 1, 117 times 0, 1, 123 times 0, 1, 129 times 0, 1, 136 times 0, 1, 143 times 0, 1, 150 times 0, 1, 157 times 0, 1, 165 times 0, 1, 174 times 0, 1, 183 times 0, 1, 192 times 0) [i] based on linear OA(534, 35, F5, 34) (dual of [35, 1, 35]-code or 35-arc in PG(33,5)), using
- dual of repetition code with length 35 [i]
- 3941 step Varšamov–Edel lengthening with (ri) = (8, 4, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 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, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 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, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 38 times 0, 1, 41 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 50 times 0, 1, 53 times 0, 1, 55 times 0, 1, 58 times 0, 1, 61 times 0, 1, 65 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 79 times 0, 1, 82 times 0, 1, 87 times 0, 1, 91 times 0, 1, 96 times 0, 1, 101 times 0, 1, 106 times 0, 1, 111 times 0, 1, 117 times 0, 1, 123 times 0, 1, 129 times 0, 1, 136 times 0, 1, 143 times 0, 1, 150 times 0, 1, 157 times 0, 1, 165 times 0, 1, 174 times 0, 1, 183 times 0, 1, 192 times 0) [i] based on linear OA(534, 35, F5, 34) (dual of [35, 1, 35]-code or 35-arc in PG(33,5)), using
(112, 112+34, 1806346)-Net in Base 5 — Upper bound on s
There is no (112, 146, 1806347)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 121041 015520 359939 556926 208251 238906 374179 851059 997013 156565 987125 100025 908763 503283 403054 847893 249005 > 5146 [i]