Best Known (48−17, 48, s)-Nets in Base 32
(48−17, 48, 429)-Net over F32 — Constructive and digital
Digital (31, 48, 429)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 33)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 with arbitrarily large s, using
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32, using
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 3, 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, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 8, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 17, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 1, 33)-net over F32, using
(48−17, 48, 2048)-Net in Base 32 — Constructive
(31, 48, 2048)-net in base 32, using
- 321 times duplication [i] based on (30, 47, 2048)-net in base 32, using
- net defined by OOA [i] based on OOA(3247, 2048, S32, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(3247, 16385, S32, 17), using
- discarding factors based on OA(3247, 16386, S32, 17), using
- discarding parts of the base [i] based on linear OA(12833, 16386, F128, 17) (dual of [16386, 16353, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(12833, 16384, F128, 17) (dual of [16384, 16351, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(16) ⊂ Ce(15) [i] based on
- discarding parts of the base [i] based on linear OA(12833, 16386, F128, 17) (dual of [16386, 16353, 18]-code), using
- discarding factors based on OA(3247, 16386, S32, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(3247, 16385, S32, 17), using
- net defined by OOA [i] based on OOA(3247, 2048, S32, 17, 17), using
(48−17, 48, 7196)-Net over F32 — Digital
Digital (31, 48, 7196)-net over F32, using
(48−17, 48, large)-Net in Base 32 — Upper bound on s
There is no (31, 48, large)-net in base 32, because
- 15 times m-reduction [i] would yield (31, 33, large)-net in base 32, but