Best Known (113−32, 113, s)-Nets in Base 9
(113−32, 113, 756)-Net over F9 — Constructive and digital
Digital (81, 113, 756)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (1, 17, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- digital (64, 96, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 48, 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, 48, 370)-net over F81, using
- digital (1, 17, 16)-net over F9, using
(113−32, 113, 5480)-Net over F9 — Digital
Digital (81, 113, 5480)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9113, 5480, F9, 32) (dual of [5480, 5367, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(9113, 6561, F9, 32) (dual of [6561, 6448, 33]-code), using
- an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- discarding factors / shortening the dual code based on linear OA(9113, 6561, F9, 32) (dual of [6561, 6448, 33]-code), using
(113−32, 113, 4664290)-Net in Base 9 — Upper bound on s
There is no (81, 113, 4664291)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 675156 658207 946745 158337 596422 789963 808210 954891 861484 573585 973516 543913 626377 812064 790426 243003 085827 048833 > 9113 [i]