Best Known (6, 6+8, s)-Nets in Base 9
(6, 6+8, 34)-Net over F9 — Constructive and digital
Digital (6, 14, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
(6, 6+8, 38)-Net in Base 9 — Constructive
(6, 14, 38)-net in base 9, using
- 1 times m-reduction [i] based on (6, 15, 38)-net in base 9, using
- base change [i] based on digital (1, 10, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- base change [i] based on digital (1, 10, 38)-net over F27, using
(6, 6+8, 42)-Net over F9 — Digital
Digital (6, 14, 42)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(914, 42, F9, 8) (dual of [42, 28, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(914, 43, F9, 8) (dual of [43, 29, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(914, 41, F9, 8) (dual of [41, 27, 9]-code), using an extension Ce(7) of the narrow-sense BCH-code C(I) with length 40 | 92−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(912, 41, F9, 7) (dual of [41, 29, 8]-code), using an extension Ce(6) of the narrow-sense BCH-code C(I) with length 40 | 92−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(90, 2, F9, 0) (dual of [2, 2, 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(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(914, 43, F9, 8) (dual of [43, 29, 9]-code), using
(6, 6+8, 603)-Net in Base 9 — Upper bound on s
There is no (6, 14, 604)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 23 016127 810689 > 914 [i]