Best Known (73, 73+28, s)-Nets in Base 9
(73, 73+28, 740)-Net over F9 — Constructive and digital
Digital (73, 101, 740)-net over F9, using
- 13 times m-reduction [i] based on digital (73, 114, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 57, 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, 57, 370)-net over F81, using
(73, 73+28, 6156)-Net over F9 — Digital
Digital (73, 101, 6156)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9101, 6156, F9, 28) (dual of [6156, 6055, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9101, 6577, F9, 28) (dual of [6577, 6476, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(23) [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(985, 6561, F9, 24) (dual of [6561, 6476, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(94, 16, F9, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,9)), using
- construction X applied to Ce(27) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(9101, 6577, F9, 28) (dual of [6577, 6476, 29]-code), using
(73, 73+28, 5788222)-Net in Base 9 — Upper bound on s
There is no (73, 101, 5788223)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 2 390527 238177 003450 218944 251853 353554 328918 806999 224428 946641 758504 874943 823573 195553 899629 929361 > 9101 [i]