Best Known (62, 62+16, s)-Nets in Base 32
(62, 62+16, 1048575)-Net over F32 — Constructive and digital
Digital (62, 78, 1048575)-net over F32, using
- 322 times duplication [i] based on digital (60, 76, 1048575)-net over F32, using
- net defined by OOA [i] based on linear OOA(3276, 1048575, F32, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3276, 8388600, F32, 16) (dual of [8388600, 8388524, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3276, large, F32, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3276, large, F32, 16) (dual of [large, large−76, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3276, 8388600, F32, 16) (dual of [8388600, 8388524, 17]-code), using
- net defined by OOA [i] based on linear OOA(3276, 1048575, F32, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
(62, 62+16, large)-Net over F32 — Digital
Digital (62, 78, large)-net over F32, using
- 322 times duplication [i] based on digital (60, 76, large)-net over F32, using
(62, 62+16, large)-Net in Base 32 — Upper bound on s
There is no (62, 78, large)-net in base 32, because
- 14 times m-reduction [i] would yield (62, 64, large)-net in base 32, but