Best Known (136−48, 136, s)-Nets in Base 9
(136−48, 136, 740)-Net over F9 — Constructive and digital
Digital (88, 136, 740)-net over F9, using
- 8 times m-reduction [i] based on digital (88, 144, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 72, 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, 72, 370)-net over F81, using
(136−48, 136, 1349)-Net over F9 — Digital
Digital (88, 136, 1349)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9136, 1349, F9, 48) (dual of [1349, 1213, 49]-code), using
- 1212 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 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, 1, 0, 0, 0, 1, 4 times 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, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 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, 16 times 0, 1, 18 times 0, 1, 19 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, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 38 times 0, 1, 39 times 0, 1, 42 times 0, 1, 43 times 0, 1, 46 times 0, 1, 49 times 0, 1, 50 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0) [i] based on linear OA(948, 49, F9, 48) (dual of [49, 1, 49]-code or 49-arc in PG(47,9)), using
- dual of repetition code with length 49 [i]
- 1212 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 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, 1, 0, 0, 0, 1, 4 times 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, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 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, 16 times 0, 1, 18 times 0, 1, 19 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, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 38 times 0, 1, 39 times 0, 1, 42 times 0, 1, 43 times 0, 1, 46 times 0, 1, 49 times 0, 1, 50 times 0, 1, 53 times 0, 1, 56 times 0, 1, 59 times 0) [i] based on linear OA(948, 49, F9, 48) (dual of [49, 1, 49]-code or 49-arc in PG(47,9)), using
(136−48, 136, 313059)-Net in Base 9 — Upper bound on s
There is no (88, 136, 313060)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 5984 098131 218895 376315 468153 347807 839941 635875 336015 531315 376840 493530 912555 620614 621808 826551 295814 956018 403941 401082 672546 983169 > 9136 [i]