Best Known (114−31, 114, s)-Nets in Base 9
(114−31, 114, 772)-Net over F9 — Constructive and digital
Digital (83, 114, 772)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 20, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (63, 94, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 47, 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, 47, 370)-net over F81, using
- digital (5, 20, 32)-net over F9, using
(114−31, 114, 6581)-Net over F9 — Digital
Digital (83, 114, 6581)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9114, 6581, F9, 31) (dual of [6581, 6467, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(9109, 6561, F9, 31) (dual of [6561, 6452, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(993, 6561, F9, 26) (dual of [6561, 6468, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(95, 20, F9, 4) (dual of [20, 15, 5]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
(114−31, 114, large)-Net in Base 9 — Upper bound on s
There is no (83, 114, large)-net in base 9, because
- 29 times m-reduction [i] would yield (83, 85, large)-net in base 9, but