Best Known (89, 134, s)-Nets in Base 9
(89, 134, 740)-Net over F9 — Constructive and digital
Digital (89, 134, 740)-net over F9, using
- 12 times m-reduction [i] based on digital (89, 146, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 73, 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, 73, 370)-net over F81, using
(89, 134, 1760)-Net over F9 — Digital
Digital (89, 134, 1760)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9134, 1760, F9, 45) (dual of [1760, 1626, 46]-code), using
- 1625 step Varšamov–Edel lengthening with (ri) = (7, 3, 1, 2, 1, 1, 1, 1, 1, 0, 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, 0, 0, 0, 1, 4 times 0, 1, 4 times 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, 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, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 28 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, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 50 times 0, 1, 52 times 0, 1, 54 times 0, 1, 58 times 0, 1, 61 times 0, 1, 64 times 0, 1, 67 times 0, 1, 71 times 0, 1, 74 times 0, 1, 79 times 0, 1, 83 times 0) [i] based on linear OA(945, 46, F9, 45) (dual of [46, 1, 46]-code or 46-arc in PG(44,9)), using
- dual of repetition code with length 46 [i]
- 1625 step Varšamov–Edel lengthening with (ri) = (7, 3, 1, 2, 1, 1, 1, 1, 1, 0, 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, 0, 0, 0, 1, 4 times 0, 1, 4 times 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, 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, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 28 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, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 50 times 0, 1, 52 times 0, 1, 54 times 0, 1, 58 times 0, 1, 61 times 0, 1, 64 times 0, 1, 67 times 0, 1, 71 times 0, 1, 74 times 0, 1, 79 times 0, 1, 83 times 0) [i] based on linear OA(945, 46, F9, 45) (dual of [46, 1, 46]-code or 46-arc in PG(44,9)), using
(89, 134, 664636)-Net in Base 9 — Upper bound on s
There is no (89, 134, 664637)-net in base 9, because
- 1 times m-reduction [i] would yield (89, 133, 664637)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 8 208483 205720 179984 011114 303774 304796 165164 549942 991469 474859 670346 002288 051382 246425 606004 315815 552549 688740 520592 559686 285105 > 9133 [i]