Best Known (8, 18, s)-Nets in Base 9
(8, 18, 40)-Net over F9 — Constructive and digital
Digital (8, 18, 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
(8, 18, 47)-Net over F9 — Digital
Digital (8, 18, 47)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(918, 47, F9, 10) (dual of [47, 29, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(918, 84, F9, 10) (dual of [84, 66, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(917, 81, F9, 10) (dual of [81, 64, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(915, 81, F9, 8) (dual of [81, 66, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(91, 3, F9, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(918, 84, F9, 10) (dual of [84, 66, 11]-code), using
(8, 18, 48)-Net in Base 9 — Constructive
(8, 18, 48)-net in base 9, using
- base change [i] based on digital (2, 12, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
(8, 18, 884)-Net in Base 9 — Upper bound on s
There is no (8, 18, 885)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 150456 062079 496137 > 918 [i]