Best Known (75, 75+30, s)-Nets in Base 9
(75, 75+30, 740)-Net over F9 — Constructive and digital
Digital (75, 105, 740)-net over F9, using
- 13 times m-reduction [i] based on digital (75, 118, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 59, 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, 59, 370)-net over F81, using
(75, 75+30, 4930)-Net over F9 — Digital
Digital (75, 105, 4930)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9105, 4930, F9, 30) (dual of [4930, 4825, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(9105, 6561, F9, 30) (dual of [6561, 6456, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(9105, 6561, F9, 30) (dual of [6561, 6456, 31]-code), using
(75, 75+30, 3840371)-Net in Base 9 — Upper bound on s
There is no (75, 105, 3840372)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 15684 282912 732117 858111 337543 488378 625057 478832 995990 636638 351732 556904 876421 923051 057341 045960 444641 > 9105 [i]