Best Known (132−43, 132, s)-Nets in Base 9
(132−43, 132, 740)-Net over F9 — Constructive and digital
Digital (89, 132, 740)-net over F9, using
- 14 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
(132−43, 132, 2081)-Net over F9 — Digital
Digital (89, 132, 2081)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9132, 2081, F9, 43) (dual of [2081, 1949, 44]-code), using
- 1948 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 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, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 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, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 37 times 0, 1, 39 times 0, 1, 41 times 0, 1, 44 times 0, 1, 46 times 0, 1, 48 times 0, 1, 51 times 0, 1, 54 times 0, 1, 57 times 0, 1, 61 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 79 times 0, 1, 83 times 0, 1, 87 times 0, 1, 93 times 0, 1, 98 times 0, 1, 103 times 0) [i] based on linear OA(943, 44, F9, 43) (dual of [44, 1, 44]-code or 44-arc in PG(42,9)), using
- dual of repetition code with length 44 [i]
- 1948 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 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, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 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, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 37 times 0, 1, 39 times 0, 1, 41 times 0, 1, 44 times 0, 1, 46 times 0, 1, 48 times 0, 1, 51 times 0, 1, 54 times 0, 1, 57 times 0, 1, 61 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 79 times 0, 1, 83 times 0, 1, 87 times 0, 1, 93 times 0, 1, 98 times 0, 1, 103 times 0) [i] based on linear OA(943, 44, F9, 43) (dual of [44, 1, 44]-code or 44-arc in PG(42,9)), using
(132−43, 132, 972865)-Net in Base 9 — Upper bound on s
There is no (89, 132, 972866)-net in base 9, because
- 1 times m-reduction [i] would yield (89, 131, 972866)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 101339 255582 848767 596316 195409 228974 847580 892116 681999 410497 601235 089907 936070 197112 543416 659782 553168 825588 315044 064117 799121 > 9131 [i]