Best Known (104, 120, s)-Nets in Base 4
(104, 120, 131072)-Net over F4 — Constructive and digital
Digital (104, 120, 131072)-net over F4, using
- net defined by OOA [i] based on linear OOA(4120, 131072, F4, 16, 16) (dual of [(131072, 16), 2097032, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4120, 1048576, F4, 16) (dual of [1048576, 1048456, 17]-code), using
- 1 times truncation [i] based on linear OA(4121, 1048577, F4, 17) (dual of [1048577, 1048456, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, 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(4121, 1048577, F4, 17) (dual of [1048577, 1048456, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(4120, 1048576, F4, 16) (dual of [1048576, 1048456, 17]-code), using
(104, 120, 524288)-Net over F4 — Digital
Digital (104, 120, 524288)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4120, 524288, F4, 2, 16) (dual of [(524288, 2), 1048456, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4120, 1048576, F4, 16) (dual of [1048576, 1048456, 17]-code), using
- 1 times truncation [i] based on linear OA(4121, 1048577, F4, 17) (dual of [1048577, 1048456, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, 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(4121, 1048577, F4, 17) (dual of [1048577, 1048456, 18]-code), using
- OOA 2-folding [i] based on linear OA(4120, 1048576, F4, 16) (dual of [1048576, 1048456, 17]-code), using
(104, 120, large)-Net in Base 4 — Upper bound on s
There is no (104, 120, large)-net in base 4, because
- 14 times m-reduction [i] would yield (104, 106, large)-net in base 4, but