Best Known (151−11, 151, s)-Nets in Base 3
(151−11, 151, 3355444)-Net over F3 — Constructive and digital
Digital (140, 151, 3355444)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- digital (135, 146, 3355440)-net over F3, using
- trace code for nets [i] based on digital (62, 73, 1677720)-net over F9, using
- net defined by OOA [i] based on linear OOA(973, 1677720, F9, 11, 11) (dual of [(1677720, 11), 18454847, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(973, 8388601, F9, 11) (dual of [8388601, 8388528, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(973, large, F9, 11) (dual of [large, large−73, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(973, large, F9, 11) (dual of [large, large−73, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(973, 8388601, F9, 11) (dual of [8388601, 8388528, 12]-code), using
- net defined by OOA [i] based on linear OOA(973, 1677720, F9, 11, 11) (dual of [(1677720, 11), 18454847, 12]-NRT-code), using
- trace code for nets [i] based on digital (62, 73, 1677720)-net over F9, using
- digital (0, 5, 4)-net over F3, using
(151−11, 151, large)-Net over F3 — Digital
Digital (140, 151, large)-net over F3, using
- t-expansion [i] based on digital (139, 151, large)-net over F3, using
- 1 times m-reduction [i] based on digital (139, 152, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3152, large, F3, 13) (dual of [large, large−152, 14]-code), using
- 31 times code embedding in larger space [i] based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 31 times code embedding in larger space [i] based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3152, large, F3, 13) (dual of [large, large−152, 14]-code), using
- 1 times m-reduction [i] based on digital (139, 152, large)-net over F3, using
(151−11, 151, large)-Net in Base 3 — Upper bound on s
There is no (140, 151, large)-net in base 3, because
- 9 times m-reduction [i] would yield (140, 142, large)-net in base 3, but