Best Known (132−18, 132, s)-Nets in Base 3
(132−18, 132, 19683)-Net over F3 — Constructive and digital
Digital (114, 132, 19683)-net over F3, using
- net defined by OOA [i] based on linear OOA(3132, 19683, F3, 18, 18) (dual of [(19683, 18), 354162, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3132, 177147, F3, 18) (dual of [177147, 177015, 19]-code), using
- 1 times truncation [i] based on linear OA(3133, 177148, F3, 19) (dual of [177148, 177015, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3133, 177148, F3, 19) (dual of [177148, 177015, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(3132, 177147, F3, 18) (dual of [177147, 177015, 19]-code), using
(132−18, 132, 59049)-Net over F3 — Digital
Digital (114, 132, 59049)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3132, 59049, F3, 3, 18) (dual of [(59049, 3), 177015, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3132, 177147, F3, 18) (dual of [177147, 177015, 19]-code), using
- 1 times truncation [i] based on linear OA(3133, 177148, F3, 19) (dual of [177148, 177015, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3133, 177148, F3, 19) (dual of [177148, 177015, 20]-code), using
- OOA 3-folding [i] based on linear OA(3132, 177147, F3, 18) (dual of [177147, 177015, 19]-code), using
(132−18, 132, large)-Net in Base 3 — Upper bound on s
There is no (114, 132, large)-net in base 3, because
- 16 times m-reduction [i] would yield (114, 116, large)-net in base 3, but