Best Known (102−28, 102, s)-Nets in Base 9
(102−28, 102, 750)-Net over F9 — Constructive and digital
Digital (74, 102, 750)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (0, 14, 10)-net over F9, using
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 0 and N(F) ≥ 10, using
- the rational function field F9(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- digital (60, 88, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 44, 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, 44, 370)-net over F81, using
- digital (0, 14, 10)-net over F9, using
(102−28, 102, 6581)-Net over F9 — Digital
Digital (74, 102, 6581)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9102, 6581, F9, 28) (dual of [6581, 6479, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- linear OA(997, 6561, F9, 28) (dual of [6561, 6464, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(981, 6561, F9, 23) (dual of [6561, 6480, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(95, 20, F9, 4) (dual of [20, 15, 5]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
(102−28, 102, 6771821)-Net in Base 9 — Upper bound on s
There is no (74, 102, 6771822)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 21 514752 227078 267135 297627 547388 794931 971391 281075 142831 212312 008995 658960 484894 674043 156889 319649 > 9102 [i]