Best Known (96, 96+37, s)-Nets in Base 9
(96, 96+37, 780)-Net over F9 — Constructive and digital
Digital (96, 133, 780)-net over F9, using
- 91 times duplication [i] based on digital (95, 132, 780)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 26, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- digital (69, 106, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 53, 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, 53, 370)-net over F81, using
- digital (8, 26, 40)-net over F9, using
- (u, u+v)-construction [i] based on
(96, 96+37, 6577)-Net over F9 — Digital
Digital (96, 133, 6577)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9133, 6577, F9, 37) (dual of [6577, 6444, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(32) [i] based on
- linear OA(9129, 6561, F9, 37) (dual of [6561, 6432, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(9117, 6561, F9, 33) (dual of [6561, 6444, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(36) ⊂ Ce(32) [i] based on
(96, 96+37, large)-Net in Base 9 — Upper bound on s
There is no (96, 133, large)-net in base 9, because
- 35 times m-reduction [i] would yield (96, 98, large)-net in base 9, but