Best Known (88, 88+43, s)-Nets in Base 9
(88, 88+43, 740)-Net over F9 — Constructive and digital
Digital (88, 131, 740)-net over F9, using
- 13 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
(88, 88+43, 1976)-Net over F9 — Digital
Digital (88, 131, 1976)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9131, 1976, F9, 43) (dual of [1976, 1845, 44]-code), using
- 1844 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) [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]
- 1844 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) [i] based on linear OA(943, 44, F9, 43) (dual of [44, 1, 44]-code or 44-arc in PG(42,9)), using
(88, 88+43, 876217)-Net in Base 9 — Upper bound on s
There is no (88, 131, 876218)-net in base 9, because
- 1 times m-reduction [i] would yield (88, 130, 876218)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 11259 855159 784750 857055 938520 162973 612034 175031 206148 003293 124902 219886 136036 434570 514711 767547 238420 623246 284666 610221 600145 > 9130 [i]