Best Known (30−5, 30, s)-Nets in Base 3
(30−5, 30, 12965)-Net over F3 — Constructive and digital
Digital (25, 30, 12965)-net over F3, using
- net defined by OOA [i] based on linear OOA(330, 12965, F3, 5, 5) (dual of [(12965, 5), 64795, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(330, 12966, F3, 2, 5) (dual of [(12966, 2), 25902, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(32, 4, F3, 2, 2) (dual of [(4, 2), 6, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;6,3) [i]
- linear OOA(328, 12962, F3, 2, 5) (dual of [(12962, 2), 25896, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(328, 25924, F3, 5) (dual of [25924, 25896, 6]-code), using
- trace code [i] based on linear OA(817, 6481, F81, 5) (dual of [6481, 6474, 6]-code), using
- OOA 2-folding [i] based on linear OA(328, 25924, F3, 5) (dual of [25924, 25896, 6]-code), using
- linear OOA(32, 4, F3, 2, 2) (dual of [(4, 2), 6, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(330, 12966, F3, 2, 5) (dual of [(12966, 2), 25902, 6]-NRT-code), using
(30−5, 30, 25928)-Net over F3 — Digital
Digital (25, 30, 25928)-net over F3, using
- net defined by OOA [i] based on linear OOA(330, 25928, F3, 5, 5) (dual of [(25928, 5), 129610, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(330, 25928, F3, 4, 5) (dual of [(25928, 4), 103682, 6]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(330, 25928, F3, 5) (dual of [25928, 25898, 6]-code), using
- (u, u+v)-construction [i] based on
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
- linear OA(328, 25924, F3, 5) (dual of [25924, 25896, 6]-code), using
- trace code [i] based on linear OA(817, 6481, F81, 5) (dual of [6481, 6474, 6]-code), using
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(330, 25928, F3, 5) (dual of [25928, 25898, 6]-code), using
- appending kth column [i] based on linear OOA(330, 25928, F3, 4, 5) (dual of [(25928, 4), 103682, 6]-NRT-code), using
(30−5, 30, 5857915)-Net in Base 3 — Upper bound on s
There is no (25, 30, 5857916)-net in base 3, because
- 1 times m-reduction [i] would yield (25, 29, 5857916)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 68 630394 873609 > 329 [i]