Best Known (211, 211+20, s)-Nets in Base 3
(211, 211+20, 838974)-Net over F3 — Constructive and digital
Digital (211, 231, 838974)-net over F3, using
- 32 times duplication [i] based on digital (209, 229, 838974)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (23, 33, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 11, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- trace code for nets [i] based on digital (1, 11, 38)-net over F27, 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 (23, 33, 114)-net over F3, using
- (u, u+v)-construction [i] based on
(211, 211+20, 4716804)-Net over F3 — Digital
Digital (211, 231, 4716804)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3231, 4716804, F3, 20) (dual of [4716804, 4716573, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3231, large, F3, 20) (dual of [large, large−231, 21]-code), using
- 35 times code embedding in larger space [i] 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]
- 35 times code embedding in larger space [i] based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3231, large, F3, 20) (dual of [large, large−231, 21]-code), using
(211, 211+20, large)-Net in Base 3 — Upper bound on s
There is no (211, 231, large)-net in base 3, because
- 18 times m-reduction [i] would yield (211, 213, large)-net in base 3, but