Best Known (94−9, 94, s)-Nets in Base 3
(94−9, 94, 2097154)-Net over F3 — Constructive and digital
Digital (85, 94, 2097154)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- digital (81, 90, 2097150)-net over F3, using
- net defined by OOA [i] based on linear OOA(390, 2097150, F3, 9, 9) (dual of [(2097150, 9), 18874260, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(390, 8388601, F3, 9) (dual of [8388601, 8388511, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(390, large, F3, 9) (dual of [large, large−90, 10]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(390, large, F3, 9) (dual of [large, large−90, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(390, 8388601, F3, 9) (dual of [8388601, 8388511, 10]-code), using
- net defined by OOA [i] based on linear OOA(390, 2097150, F3, 9, 9) (dual of [(2097150, 9), 18874260, 10]-NRT-code), using
- digital (0, 4, 4)-net over F3, using
(94−9, 94, 4194305)-Net over F3 — Digital
Digital (85, 94, 4194305)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(394, 4194305, F3, 2, 9) (dual of [(4194305, 2), 8388516, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(34, 4, F3, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;4,3) [i]
- linear OOA(390, 4194301, F3, 2, 9) (dual of [(4194301, 2), 8388512, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(390, 8388602, F3, 9) (dual of [8388602, 8388512, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(390, large, F3, 9) (dual of [large, large−90, 10]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(390, large, F3, 9) (dual of [large, large−90, 10]-code), using
- OOA 2-folding [i] based on linear OA(390, 8388602, F3, 9) (dual of [8388602, 8388512, 10]-code), using
- linear OOA(34, 4, F3, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
(94−9, 94, large)-Net in Base 3 — Upper bound on s
There is no (85, 94, large)-net in base 3, because
- 7 times m-reduction [i] would yield (85, 87, large)-net in base 3, but