Best Known (160−16, 160, s)-Nets in Base 3
(160−16, 160, 1048582)-Net over F3 — Constructive and digital
Digital (144, 160, 1048582)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (135, 151, 1048575)-net over F3, using
- net defined by OOA [i] based on linear OOA(3151, 1048575, F3, 16, 16) (dual of [(1048575, 16), 16777049, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3151, 8388600, F3, 16) (dual of [8388600, 8388449, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3151, 8388600, F3, 16) (dual of [8388600, 8388449, 17]-code), using
- net defined by OOA [i] based on linear OOA(3151, 1048575, F3, 16, 16) (dual of [(1048575, 16), 16777049, 17]-NRT-code), using
- digital (1, 9, 7)-net over F3, using
(160−16, 160, 2796208)-Net over F3 — Digital
Digital (144, 160, 2796208)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3160, 2796208, F3, 3, 16) (dual of [(2796208, 3), 8388464, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(39, 7, F3, 3, 8) (dual of [(7, 3), 12, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,12P) [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- linear OOA(3151, 2796201, F3, 3, 16) (dual of [(2796201, 3), 8388452, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 3-folding [i] based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- linear OOA(39, 7, F3, 3, 8) (dual of [(7, 3), 12, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(160−16, 160, large)-Net in Base 3 — Upper bound on s
There is no (144, 160, large)-net in base 3, because
- 14 times m-reduction [i] would yield (144, 146, large)-net in base 3, but