Best Known (25, 33, s)-Nets in Base 32
(25, 33, 262178)-Net over F32 — Constructive and digital
Digital (25, 33, 262178)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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 (21, 29, 262145)-net over F32, using
- net defined by OOA [i] based on linear OOA(3229, 262145, F32, 8, 8) (dual of [(262145, 8), 2097131, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3229, 1048580, F32, 8) (dual of [1048580, 1048551, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(3229, 1048576, F32, 8) (dual of [1048576, 1048547, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(3225, 1048576, F32, 7) (dual of [1048576, 1048551, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- OA 4-folding and stacking [i] based on linear OA(3229, 1048580, F32, 8) (dual of [1048580, 1048551, 9]-code), using
- net defined by OOA [i] based on linear OOA(3229, 262145, F32, 8, 8) (dual of [(262145, 8), 2097131, 9]-NRT-code), using
- digital (0, 4, 33)-net over F32, using
(25, 33, 524289)-Net in Base 32 — Constructive
(25, 33, 524289)-net in base 32, using
- 321 times duplication [i] based on (24, 32, 524289)-net in base 32, using
- net defined by OOA [i] based on OOA(3232, 524289, S32, 8, 8), using
- OA 4-folding and stacking [i] based on OA(3232, 2097156, S32, 8), using
- 1 times code embedding in larger space [i] based on OA(3231, 2097155, S32, 8), using
- discarding parts of the base [i] based on linear OA(12822, 2097155, F128, 8) (dual of [2097155, 2097133, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 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(7) ⊂ Ce(6) [i] based on
- discarding parts of the base [i] based on linear OA(12822, 2097155, F128, 8) (dual of [2097155, 2097133, 9]-code), using
- 1 times code embedding in larger space [i] based on OA(3231, 2097155, S32, 8), using
- OA 4-folding and stacking [i] based on OA(3232, 2097156, S32, 8), using
- net defined by OOA [i] based on OOA(3232, 524289, S32, 8, 8), using
(25, 33, 1359143)-Net over F32 — Digital
Digital (25, 33, 1359143)-net over F32, using
(25, 33, large)-Net in Base 32 — Upper bound on s
There is no (25, 33, large)-net in base 32, because
- 6 times m-reduction [i] would yield (25, 27, large)-net in base 32, but