Best Known (201, 201+20, s)-Nets in Base 3
(201, 201+20, 838900)-Net over F3 — Constructive and digital
Digital (201, 221, 838900)-net over F3, using
- 31 times duplication [i] based on digital (200, 220, 838900)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (14, 24, 40)-net over F3, using
- trace code for nets [i] based on digital (2, 12, 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, 12, 20)-net over F9, using
- digital (176, 196, 838860)-net over F3, using
- net defined by OOA [i] based on linear OOA(3196, 838860, F3, 20, 20) (dual of [(838860, 20), 16777004, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3196, 8388600, F3, 20) (dual of [8388600, 8388404, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3196, 8388600, F3, 20) (dual of [8388600, 8388404, 21]-code), using
- net defined by OOA [i] based on linear OOA(3196, 838860, F3, 20, 20) (dual of [(838860, 20), 16777004, 21]-NRT-code), using
- digital (14, 24, 40)-net over F3, using
- (u, u+v)-construction [i] based on
(201, 201+20, 4194347)-Net over F3 — Digital
Digital (201, 221, 4194347)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3221, 4194347, F3, 2, 20) (dual of [(4194347, 2), 8388473, 21]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(325, 46, F3, 2, 10) (dual of [(46, 2), 67, 11]-NRT-code), using
- linear OOA(3196, 4194301, F3, 2, 20) (dual of [(4194301, 2), 8388406, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3196, 8388602, F3, 20) (dual of [8388602, 8388406, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- OOA 2-folding [i] based on linear OA(3196, 8388602, F3, 20) (dual of [8388602, 8388406, 21]-code), using
- (u, u+v)-construction [i] based on
(201, 201+20, large)-Net in Base 3 — Upper bound on s
There is no (201, 221, large)-net in base 3, because
- 18 times m-reduction [i] would yield (201, 203, large)-net in base 3, but