Best Known (99, 99+16, s)-Nets in Base 9
(99, 99+16, 1048575)-Net over F9 — Constructive and digital
Digital (99, 115, 1048575)-net over F9, using
- 92 times duplication [i] based on digital (97, 113, 1048575)-net over F9, using
- net defined by OOA [i] based on linear OOA(9113, 1048575, F9, 16, 16) (dual of [(1048575, 16), 16777087, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(9113, 8388600, F9, 16) (dual of [8388600, 8388487, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(9113, large, F9, 16) (dual of [large, large−113, 17]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(9113, large, F9, 16) (dual of [large, large−113, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(9113, 8388600, F9, 16) (dual of [8388600, 8388487, 17]-code), using
- net defined by OOA [i] based on linear OOA(9113, 1048575, F9, 16, 16) (dual of [(1048575, 16), 16777087, 17]-NRT-code), using
(99, 99+16, large)-Net over F9 — Digital
Digital (99, 115, large)-net over F9, using
- 94 times duplication [i] based on digital (95, 111, large)-net over F9, using
(99, 99+16, large)-Net in Base 9 — Upper bound on s
There is no (99, 115, large)-net in base 9, because
- 14 times m-reduction [i] would yield (99, 101, large)-net in base 9, but