Best Known (108−16, 108, s)-Nets in Base 4
(108−16, 108, 32768)-Net over F4 — Constructive and digital
Digital (92, 108, 32768)-net over F4, using
- net defined by OOA [i] based on linear OOA(4108, 32768, F4, 16, 16) (dual of [(32768, 16), 524180, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4108, 262144, F4, 16) (dual of [262144, 262036, 17]-code), using
- 1 times truncation [i] based on linear OA(4109, 262145, F4, 17) (dual of [262145, 262036, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, 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(4109, 262145, F4, 17) (dual of [262145, 262036, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(4108, 262144, F4, 16) (dual of [262144, 262036, 17]-code), using
(108−16, 108, 131072)-Net over F4 — Digital
Digital (92, 108, 131072)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4108, 131072, F4, 2, 16) (dual of [(131072, 2), 262036, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4108, 262144, F4, 16) (dual of [262144, 262036, 17]-code), using
- 1 times truncation [i] based on linear OA(4109, 262145, F4, 17) (dual of [262145, 262036, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, 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(4109, 262145, F4, 17) (dual of [262145, 262036, 18]-code), using
- OOA 2-folding [i] based on linear OA(4108, 262144, F4, 16) (dual of [262144, 262036, 17]-code), using
(108−16, 108, large)-Net in Base 4 — Upper bound on s
There is no (92, 108, large)-net in base 4, because
- 14 times m-reduction [i] would yield (92, 94, large)-net in base 4, but