Best Known (69, 69+39, s)-Nets in Base 32
(69, 69+39, 392)-Net over F32 — Constructive and digital
Digital (69, 108, 392)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 16, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (7, 20, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 26, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 46, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 16, 98)-net over F32, using
(69, 69+39, 862)-Net in Base 32 — Constructive
(69, 108, 862)-net in base 32, using
- net defined by OOA [i] based on OOA(32108, 862, S32, 39, 39), using
- OOA 19-folding and stacking with additional row [i] based on OA(32108, 16379, S32, 39), using
- discarding factors based on OA(32108, 16386, S32, 39), using
- discarding parts of the base [i] based on linear OA(12877, 16386, F128, 39) (dual of [16386, 16309, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(37) [i] based on
- linear OA(12877, 16384, F128, 39) (dual of [16384, 16307, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(12875, 16384, F128, 38) (dual of [16384, 16309, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(38) ⊂ Ce(37) [i] based on
- discarding parts of the base [i] based on linear OA(12877, 16386, F128, 39) (dual of [16386, 16309, 40]-code), using
- discarding factors based on OA(32108, 16386, S32, 39), using
- OOA 19-folding and stacking with additional row [i] based on OA(32108, 16379, S32, 39), using
(69, 69+39, 9207)-Net over F32 — Digital
Digital (69, 108, 9207)-net over F32, using
(69, 69+39, large)-Net in Base 32 — Upper bound on s
There is no (69, 108, large)-net in base 32, because
- 37 times m-reduction [i] would yield (69, 71, large)-net in base 32, but