Best Known (98, 98+38, s)-Nets in Base 9
(98, 98+38, 780)-Net over F9 — Constructive and digital
Digital (98, 136, 780)-net over F9, using
- 1 times m-reduction [i] based on digital (98, 137, 780)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 27, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- digital (71, 110, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 55, 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, 55, 370)-net over F81, using
- digital (8, 27, 40)-net over F9, using
- (u, u+v)-construction [i] based on
(98, 98+38, 6573)-Net over F9 — Digital
Digital (98, 136, 6573)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9136, 6573, F9, 38) (dual of [6573, 6437, 39]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9135, 6571, F9, 38) (dual of [6571, 6436, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(34) [i] based on
- linear OA(9133, 6561, F9, 38) (dual of [6561, 6428, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(9125, 6561, F9, 35) (dual of [6561, 6436, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- construction X applied to Ce(37) ⊂ Ce(34) [i] based on
- linear OA(9135, 6572, F9, 37) (dual of [6572, 6437, 38]-code), using Gilbert–Varšamov bound and bm = 9135 > Vbs−1(k−1) = 215 785760 243328 688895 412539 419023 084590 316669 241974 614161 682328 431859 813538 631038 595200 326265 783023 917724 706400 872067 353244 379417 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(9135, 6571, F9, 38) (dual of [6571, 6436, 39]-code), using
- construction X with Varšamov bound [i] based on
(98, 98+38, 6706442)-Net in Base 9 — Upper bound on s
There is no (98, 136, 6706443)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 5983 863037 325554 599904 333966 108410 892714 294405 971462 845383 139562 686832 390304 451349 737158 034189 847841 471595 350960 697252 338429 984777 > 9136 [i]