Best Known (121−33, 121, s)-Nets in Base 9
(121−33, 121, 776)-Net over F9 — Constructive and digital
Digital (88, 121, 776)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (7, 23, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- digital (65, 98, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 49, 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, 49, 370)-net over F81, using
- digital (7, 23, 36)-net over F9, using
(121−33, 121, 6581)-Net over F9 — Digital
Digital (88, 121, 6581)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9121, 6581, F9, 33) (dual of [6581, 6460, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(28) [i] based on
- 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(9101, 6561, F9, 29) (dual of [6561, 6460, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(94, 20, F9, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,9)), using
- construction X applied to Ce(32) ⊂ Ce(28) [i] based on
(121−33, 121, large)-Net in Base 9 — Upper bound on s
There is no (88, 121, large)-net in base 9, because
- 31 times m-reduction [i] would yield (88, 90, large)-net in base 9, but