Best Known (117−7, 117, s)-Nets in Base 3
(117−7, 117, large)-Net over F3 — Constructive and digital
Digital (110, 117, large)-net over F3, using
- 317 times duplication [i] based on digital (93, 100, large)-net over F3, using
- trace code for nets [i] based on digital (43, 50, 5592401)-net over F9, using
- net defined by OOA [i] based on linear OOA(950, 5592401, F9, 9, 7) (dual of [(5592401, 9), 50331559, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(950, 5592402, F9, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
- trace code [i] based on linear OOA(8125, 2796201, F81, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8125, large, F81, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8125, large, F81, 7) (dual of [large, large−25, 8]-code), using
- trace code [i] based on linear OOA(8125, 2796201, F81, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(950, 5592402, F9, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(950, 5592401, F9, 9, 7) (dual of [(5592401, 9), 50331559, 8]-NRT-code), using
- trace code for nets [i] based on digital (43, 50, 5592401)-net over F9, using
(117−7, 117, large)-Net in Base 3 — Upper bound on s
There is no (110, 117, large)-net in base 3, because
- 5 times m-reduction [i] would yield (110, 112, large)-net in base 3, but