Best Known (96, 96+44, s)-Nets in Base 9
(96, 96+44, 740)-Net over F9 — Constructive and digital
Digital (96, 140, 740)-net over F9, using
- t-expansion [i] based on digital (91, 140, 740)-net over F9, using
- 10 times m-reduction [i] based on digital (91, 150, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 75, 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, 75, 370)-net over F81, using
- 10 times m-reduction [i] based on digital (91, 150, 740)-net over F9, using
(96, 96+44, 2721)-Net over F9 — Digital
Digital (96, 140, 2721)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9140, 2721, F9, 44) (dual of [2721, 2581, 45]-code), using
- 2580 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) [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]
- 2580 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) [i] based on linear OA(944, 45, F9, 44) (dual of [45, 1, 45]-code or 45-arc in PG(43,9)), using
(96, 96+44, 1337245)-Net in Base 9 — Upper bound on s
There is no (96, 140, 1337246)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 39 260565 918110 219938 339225 558113 119206 362944 935463 077588 402258 398281 767548 999117 774364 801336 710503 819545 434506 251284 844987 553456 321121 > 9140 [i]