Best Known (53, 53+21, s)-Nets in Base 32
(53, 53+21, 3341)-Net over F32 — Constructive and digital
Digital (53, 74, 3341)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (40, 61, 3277)-net over F32, using
- net defined by OOA [i] based on linear OOA(3261, 3277, F32, 21, 21) (dual of [(3277, 21), 68756, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3261, 32771, F32, 21) (dual of [32771, 32710, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(3261, 32768, F32, 21) (dual of [32768, 32707, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(20) ⊂ Ce(19) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(3261, 32771, F32, 21) (dual of [32771, 32710, 22]-code), using
- net defined by OOA [i] based on linear OOA(3261, 3277, F32, 21, 21) (dual of [(3277, 21), 68756, 22]-NRT-code), using
- digital (3, 13, 64)-net over F32, using
(53, 53+21, 26214)-Net in Base 32 — Constructive
(53, 74, 26214)-net in base 32, using
- net defined by OOA [i] based on OOA(3274, 26214, S32, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3274, 262141, S32, 21), using
- discarding factors based on OA(3274, 262147, S32, 21), using
- discarding parts of the base [i] based on linear OA(6461, 262147, F64, 21) (dual of [262147, 262086, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(6461, 262144, F64, 21) (dual of [262144, 262083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(6461, 262147, F64, 21) (dual of [262147, 262086, 22]-code), using
- discarding factors based on OA(3274, 262147, S32, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3274, 262141, S32, 21), using
(53, 53+21, 99321)-Net over F32 — Digital
Digital (53, 74, 99321)-net over F32, using
(53, 53+21, large)-Net in Base 32 — Upper bound on s
There is no (53, 74, large)-net in base 32, because
- 19 times m-reduction [i] would yield (53, 55, large)-net in base 32, but