Best Known (81, 81+10, s)-Nets in Base 3
(81, 81+10, 1677720)-Net over F3 — Constructive and digital
Digital (81, 91, 1677720)-net over F3, using
- net defined by OOA [i] based on linear OOA(391, 1677720, F3, 10, 10) (dual of [(1677720, 10), 16777109, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(391, 8388600, F3, 10) (dual of [8388600, 8388509, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(391, 8388600, F3, 10) (dual of [8388600, 8388509, 11]-code), using
(81, 81+10, 2796201)-Net over F3 — Digital
Digital (81, 91, 2796201)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(391, 2796201, F3, 3, 10) (dual of [(2796201, 3), 8388512, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 3-folding [i] based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
(81, 81+10, large)-Net in Base 3 — Upper bound on s
There is no (81, 91, large)-net in base 3, because
- 8 times m-reduction [i] would yield (81, 83, large)-net in base 3, but