Best Known (185, 185+18, s)-Nets in Base 3
(185, 185+18, 932107)-Net over F3 — Constructive and digital
Digital (185, 203, 932107)-net over F3, using
- 31 times duplication [i] based on digital (184, 202, 932107)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (13, 22, 40)-net over F3, using
- trace code for nets [i] based on digital (2, 11, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- trace code for nets [i] based on digital (2, 11, 20)-net over F9, using
- digital (162, 180, 932067)-net over F3, using
- net defined by OOA [i] based on linear OOA(3180, 932067, F3, 18, 18) (dual of [(932067, 18), 16777026, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- net defined by OOA [i] based on linear OOA(3180, 932067, F3, 18, 18) (dual of [(932067, 18), 16777026, 19]-NRT-code), using
- digital (13, 22, 40)-net over F3, using
- (u, u+v)-construction [i] based on
(185, 185+18, 4194350)-Net over F3 — Digital
Digital (185, 203, 4194350)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3203, 4194350, F3, 2, 18) (dual of [(4194350, 2), 8388497, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(323, 49, F3, 2, 9) (dual of [(49, 2), 75, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(323, 49, F3, 9) (dual of [49, 26, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 53, F3, 9) (dual of [53, 30, 10]-code), using
- 7 times truncation [i] based on linear OA(330, 60, F3, 16) (dual of [60, 30, 17]-code), using
- strength reduction [i] based on linear OA(330, 60, F3, 17) (dual of [60, 30, 18]-code), using
- extended quadratic residue code Qe(60,3) [i]
- strength reduction [i] based on linear OA(330, 60, F3, 17) (dual of [60, 30, 18]-code), using
- 7 times truncation [i] based on linear OA(330, 60, F3, 16) (dual of [60, 30, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 53, F3, 9) (dual of [53, 30, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(323, 49, F3, 9) (dual of [49, 26, 10]-code), using
- linear OOA(3180, 4194301, F3, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-code), using
- linear OOA(323, 49, F3, 2, 9) (dual of [(49, 2), 75, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
(185, 185+18, large)-Net in Base 3 — Upper bound on s
There is no (185, 203, large)-net in base 3, because
- 16 times m-reduction [i] would yield (185, 187, large)-net in base 3, but