Best Known (234, 234+16, s)-Nets in Base 3
(234, 234+16, 4194300)-Net over F3 — Constructive and digital
Digital (234, 250, 4194300)-net over F3, using
- 32 times duplication [i] based on digital (232, 248, 4194300)-net over F3, using
- net defined by OOA [i] based on linear OOA(3248, 4194300, F3, 20, 16) (dual of [(4194300, 20), 83885752, 17]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3248, 8388601, F3, 4, 16) (dual of [(8388601, 4), 33554156, 17]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3244, 8388600, F3, 4, 16) (dual of [(8388600, 4), 33554156, 17]-NRT-code), using
- trace code [i] based on linear OOA(8161, 2097150, F81, 4, 16) (dual of [(2097150, 4), 8388539, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8161, 8388600, F81, 16) (dual of [8388600, 8388539, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(8161, large, F81, 16) (dual of [large, large−61, 17]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(8161, large, F81, 16) (dual of [large, large−61, 17]-code), using
- OOA 4-folding [i] based on linear OA(8161, 8388600, F81, 16) (dual of [8388600, 8388539, 17]-code), using
- trace code [i] based on linear OOA(8161, 2097150, F81, 4, 16) (dual of [(2097150, 4), 8388539, 17]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3244, 8388600, F3, 4, 16) (dual of [(8388600, 4), 33554156, 17]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3248, 8388601, F3, 4, 16) (dual of [(8388601, 4), 33554156, 17]-NRT-code), using
- net defined by OOA [i] based on linear OOA(3248, 4194300, F3, 20, 16) (dual of [(4194300, 20), 83885752, 17]-NRT-code), using
(234, 234+16, large)-Net over F3 — Digital
Digital (234, 250, large)-net over F3, using
- 39 times duplication [i] based on digital (225, 241, large)-net over F3, using
- t-expansion [i] based on digital (221, 241, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F3, 20) (dual of [large, large−241, 21]-code), using
- strength reduction [i] based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- strength reduction [i] based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F3, 20) (dual of [large, large−241, 21]-code), using
- t-expansion [i] based on digital (221, 241, large)-net over F3, using
(234, 234+16, large)-Net in Base 3 — Upper bound on s
There is no (234, 250, large)-net in base 3, because
- 14 times m-reduction [i] would yield (234, 236, large)-net in base 3, but