Best Known (167, 183, s)-Nets in Base 3
(167, 183, 1048903)-Net over F3 — Constructive and digital
Digital (167, 183, 1048903)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (24, 32, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 8, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 8, 82)-net over F81, 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 (24, 32, 328)-net over F3, using
(167, 183, 4819510)-Net over F3 — Digital
Digital (167, 183, 4819510)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3183, 4819510, F3, 16) (dual of [4819510, 4819327, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3183, large, F3, 16) (dual of [large, large−183, 17]-code), using
- 32 times code embedding in larger space [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]
- 32 times code embedding in larger space [i] based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3183, large, F3, 16) (dual of [large, large−183, 17]-code), using
(167, 183, large)-Net in Base 3 — Upper bound on s
There is no (167, 183, large)-net in base 3, because
- 14 times m-reduction [i] would yield (167, 169, large)-net in base 3, but