Best Known (98−16, 98, s)-Nets in Base 8
(98−16, 98, 262144)-Net over F8 — Constructive and digital
Digital (82, 98, 262144)-net over F8, using
- net defined by OOA [i] based on linear OOA(898, 262144, F8, 16, 16) (dual of [(262144, 16), 4194206, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(898, 2097152, F8, 16) (dual of [2097152, 2097054, 17]-code), using
- 1 times truncation [i] based on linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(898, 2097152, F8, 16) (dual of [2097152, 2097054, 17]-code), using
(98−16, 98, 1561281)-Net over F8 — Digital
Digital (82, 98, 1561281)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(898, 1561281, F8, 16) (dual of [1561281, 1561183, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(898, 2097152, F8, 16) (dual of [2097152, 2097054, 17]-code), using
- 1 times truncation [i] based on linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(898, 2097152, F8, 16) (dual of [2097152, 2097054, 17]-code), using
(98−16, 98, large)-Net in Base 8 — Upper bound on s
There is no (82, 98, large)-net in base 8, because
- 14 times m-reduction [i] would yield (82, 84, large)-net in base 8, but