Best Known (37−11, 37, s)-Nets in Base 32
(37−11, 37, 6598)-Net over F32 — Constructive and digital
Digital (26, 37, 6598)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 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 (20, 31, 6554)-net over F32, using
- net defined by OOA [i] based on linear OOA(3231, 6554, F32, 11, 11) (dual of [(6554, 11), 72063, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3231, 32771, F32, 11) (dual of [32771, 32740, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(3231, 32768, F32, 11) (dual of [32768, 32737, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(3228, 32768, F32, 10) (dual of [32768, 32740, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 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(10) ⊂ Ce(9) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(3231, 32771, F32, 11) (dual of [32771, 32740, 12]-code), using
- net defined by OOA [i] based on linear OOA(3231, 6554, F32, 11, 11) (dual of [(6554, 11), 72063, 12]-NRT-code), using
- digital (1, 6, 44)-net over F32, using
(37−11, 37, 13108)-Net in Base 32 — Constructive
(26, 37, 13108)-net in base 32, using
- 321 times duplication [i] based on (25, 36, 13108)-net in base 32, using
- net defined by OOA [i] based on OOA(3236, 13108, S32, 11, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(3236, 65541, S32, 11), using
- discarding factors based on OA(3236, 65542, S32, 11), using
- discarding parts of the base [i] based on linear OA(25622, 65542, F256, 11) (dual of [65542, 65520, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- discarding parts of the base [i] based on linear OA(25622, 65542, F256, 11) (dual of [65542, 65520, 12]-code), using
- discarding factors based on OA(3236, 65542, S32, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(3236, 65541, S32, 11), using
- net defined by OOA [i] based on OOA(3236, 13108, S32, 11, 11), using
(37−11, 37, 54164)-Net over F32 — Digital
Digital (26, 37, 54164)-net over F32, using
(37−11, 37, large)-Net in Base 32 — Upper bound on s
There is no (26, 37, large)-net in base 32, because
- 9 times m-reduction [i] would yield (26, 28, large)-net in base 32, but