Best Known (87−13, 87, s)-Nets in Base 9
(87−13, 87, 797190)-Net over F9 — Constructive and digital
Digital (74, 87, 797190)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- digital (65, 78, 797162)-net over F9, using
- net defined by OOA [i] based on linear OOA(978, 797162, F9, 13, 13) (dual of [(797162, 13), 10363028, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(978, 4782973, F9, 13) (dual of [4782973, 4782895, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(978, 4782976, F9, 13) (dual of [4782976, 4782898, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(978, 4782976, F9, 13) (dual of [4782976, 4782898, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(978, 4782973, F9, 13) (dual of [4782973, 4782895, 14]-code), using
- net defined by OOA [i] based on linear OOA(978, 797162, F9, 13, 13) (dual of [(797162, 13), 10363028, 14]-NRT-code), using
- digital (3, 9, 28)-net over F9, using
(87−13, 87, 5476840)-Net over F9 — Digital
Digital (74, 87, 5476840)-net over F9, using
(87−13, 87, large)-Net in Base 9 — Upper bound on s
There is no (74, 87, large)-net in base 9, because
- 11 times m-reduction [i] would yield (74, 76, large)-net in base 9, but