Best Known (173, 197, s)-Nets in Base 4
(173, 197, 87398)-Net over F4 — Constructive and digital
Digital (173, 197, 87398)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 17, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (156, 180, 87381)-net over F4, using
- net defined by OOA [i] based on linear OOA(4180, 87381, F4, 24, 24) (dual of [(87381, 24), 2096964, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4180, 1048572, F4, 24) (dual of [1048572, 1048392, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, 1048576, F4, 24) (dual of [1048576, 1048396, 25]-code), using
- 1 times truncation [i] based on linear OA(4181, 1048577, F4, 25) (dual of [1048577, 1048396, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4181, 1048577, F4, 25) (dual of [1048577, 1048396, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, 1048576, F4, 24) (dual of [1048576, 1048396, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(4180, 1048572, F4, 24) (dual of [1048572, 1048392, 25]-code), using
- net defined by OOA [i] based on linear OOA(4180, 87381, F4, 24, 24) (dual of [(87381, 24), 2096964, 25]-NRT-code), using
- digital (5, 17, 17)-net over F4, using
(173, 197, 697474)-Net over F4 — Digital
Digital (173, 197, 697474)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4197, 697474, F4, 24) (dual of [697474, 697277, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4197, 1048653, F4, 24) (dual of [1048653, 1048456, 25]-code), using
- construction X applied to C([0,12]) ⊂ C([0,8]) [i] based on
- linear OA(4181, 1048577, F4, 25) (dual of [1048577, 1048396, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 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]
- linear OA(416, 76, F4, 6) (dual of [76, 60, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 85, F4, 6) (dual of [85, 69, 7]-code), using
- construction X applied to C([0,12]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4197, 1048653, F4, 24) (dual of [1048653, 1048456, 25]-code), using
(173, 197, large)-Net in Base 4 — Upper bound on s
There is no (173, 197, large)-net in base 4, because
- 22 times m-reduction [i] would yield (173, 175, large)-net in base 4, but