Best Known (14−8, 14, s)-Nets in Base 32
(14−8, 14, 99)-Net over F32 — Constructive and digital
Digital (6, 14, 99)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 33)-net over F32, using
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (0, 8, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
(14−8, 14, 119)-Net over F32 — Digital
Digital (6, 14, 119)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3214, 119, F32, 8) (dual of [119, 105, 9]-code), using
- 22 step Varšamov–Edel lengthening with (ri) = (1, 21 times 0) [i] based on linear OA(3213, 96, F32, 8) (dual of [96, 83, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(3213, 94, F32, 8) (dual of [94, 81, 9]-code), using an extension Ce(7) of the narrow-sense BCH-code C(I) with length 93 | 322−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(3211, 94, F32, 7) (dual of [94, 83, 8]-code), using an extension Ce(6) of the narrow-sense BCH-code C(I) with length 93 | 322−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- 22 step Varšamov–Edel lengthening with (ri) = (1, 21 times 0) [i] based on linear OA(3213, 96, F32, 8) (dual of [96, 83, 9]-code), using
(14−8, 14, 257)-Net in Base 32 — Constructive
(6, 14, 257)-net in base 32, using
- 2 times m-reduction [i] based on (6, 16, 257)-net in base 32, using
- base change [i] based on digital (0, 10, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 10, 257)-net over F256, using
(14−8, 14, 13233)-Net in Base 32 — Upper bound on s
There is no (6, 14, 13234)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1180 902033 675388 858692 > 3214 [i]