Best Known (29, 38, s)-Nets in Base 32
(29, 38, 262188)-Net over F32 — Constructive and digital
Digital (29, 38, 262188)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (24, 33, 262144)-net over F32, using
- net defined by OOA [i] based on linear OOA(3233, 262144, F32, 9, 9) (dual of [(262144, 9), 2359263, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3233, 1048577, F32, 9) (dual of [1048577, 1048544, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(3233, 1048577, F32, 9) (dual of [1048577, 1048544, 10]-code), using
- net defined by OOA [i] based on linear OOA(3233, 262144, F32, 9, 9) (dual of [(262144, 9), 2359263, 10]-NRT-code), using
- digital (1, 5, 44)-net over F32, using
(29, 38, 524290)-Net in Base 32 — Constructive
(29, 38, 524290)-net in base 32, using
- net defined by OOA [i] based on OOA(3238, 524290, S32, 9, 9), using
- OOA 4-folding and stacking with additional row [i] based on OA(3238, 2097161, S32, 9), using
- discarding factors based on OA(3238, 2097163, S32, 9), using
- discarding parts of the base [i] based on linear OA(12827, 2097163, F128, 9) (dual of [2097163, 2097136, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- discarding parts of the base [i] based on linear OA(12827, 2097163, F128, 9) (dual of [2097163, 2097136, 10]-code), using
- discarding factors based on OA(3238, 2097163, S32, 9), using
- OOA 4-folding and stacking with additional row [i] based on OA(3238, 2097161, S32, 9), using
(29, 38, 1713136)-Net over F32 — Digital
Digital (29, 38, 1713136)-net over F32, using
(29, 38, large)-Net in Base 32 — Upper bound on s
There is no (29, 38, large)-net in base 32, because
- 7 times m-reduction [i] would yield (29, 31, large)-net in base 32, but