Best Known (104, 104+44, s)-Nets in Base 9
(104, 104+44, 774)-Net over F9 — Constructive and digital
Digital (104, 148, 774)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 28, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- digital (76, 120, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 60, 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, 60, 370)-net over F81, using
- digital (6, 28, 34)-net over F9, using
(104, 104+44, 4084)-Net over F9 — Digital
Digital (104, 148, 4084)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9148, 4084, F9, 44) (dual of [4084, 3936, 45]-code), using
- 3935 step Varšamov–Edel lengthening with (ri) = (7, 2, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 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, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 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, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 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, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 36 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 51 times 0, 1, 55 times 0, 1, 57 times 0, 1, 61 times 0, 1, 63 times 0, 1, 68 times 0, 1, 70 times 0, 1, 75 times 0, 1, 79 times 0, 1, 83 times 0, 1, 87 times 0, 1, 92 times 0, 1, 97 times 0, 1, 102 times 0, 1, 108 times 0, 1, 113 times 0, 1, 119 times 0, 1, 126 times 0, 1, 133 times 0, 1, 139 times 0, 1, 147 times 0, 1, 155 times 0, 1, 163 times 0, 1, 171 times 0, 1, 181 times 0, 1, 190 times 0, 1, 201 times 0) [i] based on linear OA(944, 45, F9, 44) (dual of [45, 1, 45]-code or 45-arc in PG(43,9)), using
- dual of repetition code with length 45 [i]
- 3935 step Varšamov–Edel lengthening with (ri) = (7, 2, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 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, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 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, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 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, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 36 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 51 times 0, 1, 55 times 0, 1, 57 times 0, 1, 61 times 0, 1, 63 times 0, 1, 68 times 0, 1, 70 times 0, 1, 75 times 0, 1, 79 times 0, 1, 83 times 0, 1, 87 times 0, 1, 92 times 0, 1, 97 times 0, 1, 102 times 0, 1, 108 times 0, 1, 113 times 0, 1, 119 times 0, 1, 126 times 0, 1, 133 times 0, 1, 139 times 0, 1, 147 times 0, 1, 155 times 0, 1, 163 times 0, 1, 171 times 0, 1, 181 times 0, 1, 190 times 0, 1, 201 times 0) [i] based on linear OA(944, 45, F9, 44) (dual of [45, 1, 45]-code or 45-arc in PG(43,9)), using
(104, 104+44, 2973108)-Net in Base 9 — Upper bound on s
There is no (104, 148, 2973109)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1690 028376 414746 995284 858700 529283 689962 075120 779766 653457 313385 335503 891649 678164 017602 891835 045238 004708 411893 498973 125902 838397 244745 049265 > 9148 [i]