Best Known (201−18, 201, s)-Nets in Base 3
(201−18, 201, 932099)-Net over F3 — Constructive and digital
Digital (183, 201, 932099)-net over F3, using
- 31 times duplication [i] based on digital (182, 200, 932099)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (11, 20, 32)-net over F3, using
- trace code for nets [i] based on digital (1, 10, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- trace code for nets [i] based on digital (1, 10, 16)-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 (11, 20, 32)-net over F3, using
- (u, u+v)-construction [i] based on
(201−18, 201, 4194336)-Net over F3 — Digital
Digital (183, 201, 4194336)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3201, 4194336, F3, 2, 18) (dual of [(4194336, 2), 8388471, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(321, 35, F3, 2, 9) (dual of [(35, 2), 49, 10]-NRT-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
- (u, u+v)-construction [i] based on
(201−18, 201, large)-Net in Base 3 — Upper bound on s
There is no (183, 201, large)-net in base 3, because
- 16 times m-reduction [i] would yield (183, 185, large)-net in base 3, but