Best Known (53, 53+28, s)-Nets in Base 32
(53, 53+28, 363)-Net over F32 — Constructive and digital
Digital (53, 81, 363)-net over F32, using
- 1 times m-reduction [i] based on digital (53, 82, 363)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- 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, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 4, 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, 9, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 14, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 29, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- generalized (u, u+v)-construction [i] based on
(53, 53+28, 1170)-Net in Base 32 — Constructive
(53, 81, 1170)-net in base 32, using
- 321 times duplication [i] based on (52, 80, 1170)-net in base 32, using
- t-expansion [i] based on (51, 80, 1170)-net in base 32, using
- net defined by OOA [i] based on OOA(3280, 1170, S32, 29, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(3280, 16381, S32, 29), using
- discarding factors based on OA(3280, 16386, S32, 29), using
- discarding parts of the base [i] based on linear OA(12857, 16386, F128, 29) (dual of [16386, 16329, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(28) ⊂ Ce(27) [i] based on
- discarding parts of the base [i] based on linear OA(12857, 16386, F128, 29) (dual of [16386, 16329, 30]-code), using
- discarding factors based on OA(3280, 16386, S32, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(3280, 16381, S32, 29), using
- net defined by OOA [i] based on OOA(3280, 1170, S32, 29, 29), using
- t-expansion [i] based on (51, 80, 1170)-net in base 32, using
(53, 53+28, 11561)-Net over F32 — Digital
Digital (53, 81, 11561)-net over F32, using
(53, 53+28, large)-Net in Base 32 — Upper bound on s
There is no (53, 81, large)-net in base 32, because
- 26 times m-reduction [i] would yield (53, 55, large)-net in base 32, but