Best Known (38, 38+12, s)-Nets in Base 32
(38, 38+12, 174767)-Net over F32 — Constructive and digital
Digital (38, 50, 174767)-net over F32, using
- net defined by OOA [i] based on linear OOA(3250, 174767, F32, 12, 12) (dual of [(174767, 12), 2097154, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3250, 1048602, F32, 12) (dual of [1048602, 1048552, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3250, 1048605, F32, 12) (dual of [1048605, 1048555, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(5) [i] based on
- linear OA(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(325, 29, F32, 5) (dual of [29, 24, 6]-code or 29-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- construction X applied to Ce(11) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(3250, 1048605, F32, 12) (dual of [1048605, 1048555, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3250, 1048602, F32, 12) (dual of [1048602, 1048552, 13]-code), using
(38, 38+12, 349526)-Net in Base 32 — Constructive
(38, 50, 349526)-net in base 32, using
- 321 times duplication [i] based on (37, 49, 349526)-net in base 32, using
- base change [i] based on digital (23, 35, 349526)-net over F128, using
- net defined by OOA [i] based on linear OOA(12835, 349526, F128, 12, 12) (dual of [(349526, 12), 4194277, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(12835, 2097156, F128, 12) (dual of [2097156, 2097121, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12835, 2097159, F128, 12) (dual of [2097159, 2097124, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(12835, 2097159, F128, 12) (dual of [2097159, 2097124, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(12835, 2097156, F128, 12) (dual of [2097156, 2097121, 13]-code), using
- net defined by OOA [i] based on linear OOA(12835, 349526, F128, 12, 12) (dual of [(349526, 12), 4194277, 13]-NRT-code), using
- base change [i] based on digital (23, 35, 349526)-net over F128, using
(38, 38+12, 1099627)-Net over F32 — Digital
Digital (38, 50, 1099627)-net over F32, using
(38, 38+12, large)-Net in Base 32 — Upper bound on s
There is no (38, 50, large)-net in base 32, because
- 10 times m-reduction [i] would yield (38, 40, large)-net in base 32, but