Best Known (97−10, 97, s)-Nets in Base 3
(97−10, 97, 1677727)-Net over F3 — Constructive and digital
Digital (87, 97, 1677727)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- 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
- net defined by OOA [i] based on linear OOA(391, 1677720, F3, 10, 10) (dual of [(1677720, 10), 16777109, 11]-NRT-code), using
- digital (1, 6, 7)-net over F3, using
(97−10, 97, 4194308)-Net over F3 — Digital
Digital (87, 97, 4194308)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(397, 4194308, F3, 2, 10) (dual of [(4194308, 2), 8388519, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(36, 7, F3, 2, 5) (dual of [(7, 2), 8, 6]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,8P) [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- linear OOA(391, 4194301, F3, 2, 10) (dual of [(4194301, 2), 8388511, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(391, 8388602, F3, 10) (dual of [8388602, 8388511, 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
- OOA 2-folding [i] based on linear OA(391, 8388602, F3, 10) (dual of [8388602, 8388511, 11]-code), using
- linear OOA(36, 7, F3, 2, 5) (dual of [(7, 2), 8, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
(97−10, 97, large)-Net in Base 3 — Upper bound on s
There is no (87, 97, large)-net in base 3, because
- 8 times m-reduction [i] would yield (87, 89, large)-net in base 3, but