Best Known (83−5, 83, s)-Nets in Base 3
(83−5, 83, large)-Net over F3 — Constructive and digital
Digital (78, 83, large)-net over F3, using
- 1 times m-reduction [i] based on digital (78, 84, large)-net over F3, using
- trace code for nets [i] based on digital (36, 42, 5592401)-net over F9, using
- net defined by OOA [i] based on linear OOA(942, 5592401, F9, 9, 6) (dual of [(5592401, 9), 50331567, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(942, 5592402, F9, 3, 6) (dual of [(5592402, 3), 16777164, 7]-NRT-code), using
- trace code [i] based on linear OOA(8121, 2796201, F81, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8121, large, F81, 6) (dual of [large, large−21, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding [i] based on linear OA(8121, large, F81, 6) (dual of [large, large−21, 7]-code), using
- trace code [i] based on linear OOA(8121, 2796201, F81, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(942, 5592402, F9, 3, 6) (dual of [(5592402, 3), 16777164, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(942, 5592401, F9, 9, 6) (dual of [(5592401, 9), 50331567, 7]-NRT-code), using
- trace code for nets [i] based on digital (36, 42, 5592401)-net over F9, using
(83−5, 83, large)-Net in Base 3 — Upper bound on s
There is no (78, 83, large)-net in base 3, because
- 3 times m-reduction [i] would yield (78, 80, large)-net in base 3, but