Best Known (30, 30+16, s)-Nets in Base 32
(30, 30+16, 4096)-Net over F32 — Constructive and digital
Digital (30, 46, 4096)-net over F32, using
- net defined by OOA [i] based on linear OOA(3246, 4096, F32, 16, 16) (dual of [(4096, 16), 65490, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3246, 32768, F32, 16) (dual of [32768, 32722, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OA 8-folding and stacking [i] based on linear OA(3246, 32768, F32, 16) (dual of [32768, 32722, 17]-code), using
(30, 30+16, 16385)-Net over F32 — Digital
Digital (30, 46, 16385)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3246, 16385, F32, 2, 16) (dual of [(16385, 2), 32724, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3246, 32770, F32, 16) (dual of [32770, 32724, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 32771, F32, 16) (dual of [32771, 32725, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(3246, 32768, F32, 16) (dual of [32768, 32722, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3243, 32768, F32, 15) (dual of [32768, 32725, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(15) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(3246, 32771, F32, 16) (dual of [32771, 32725, 17]-code), using
- OOA 2-folding [i] based on linear OA(3246, 32770, F32, 16) (dual of [32770, 32724, 17]-code), using
(30, 30+16, large)-Net in Base 32 — Upper bound on s
There is no (30, 46, large)-net in base 32, because
- 14 times m-reduction [i] would yield (30, 32, large)-net in base 32, but