Best Known (40−15, 40, s)-Nets in Base 32
(40−15, 40, 330)-Net over F32 — Constructive and digital
Digital (25, 40, 330)-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, 2, 33)-net over F32, using
- 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, 3, 33)-net 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, 7, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 15, 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
(40−15, 40, 587)-Net in Base 32 — Constructive
(25, 40, 587)-net in base 32, using
- net defined by OOA [i] based on OOA(3240, 587, S32, 15, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(3240, 4110, S32, 15), using
- discarding parts of the base [i] based on linear OA(6433, 4110, F64, 15) (dual of [4110, 4077, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(6429, 4096, F64, 15) (dual of [4096, 4067, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(644, 14, F64, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- discarding parts of the base [i] based on linear OA(6433, 4110, F64, 15) (dual of [4110, 4077, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on OA(3240, 4110, S32, 15), using
(40−15, 40, 3902)-Net over F32 — Digital
Digital (25, 40, 3902)-net over F32, using
(40−15, 40, large)-Net in Base 32 — Upper bound on s
There is no (25, 40, large)-net in base 32, because
- 13 times m-reduction [i] would yield (25, 27, large)-net in base 32, but