Best Known (161−16, 161, s)-Nets in Base 3
(161−16, 161, 1048583)-Net over F3 — Constructive and digital
Digital (145, 161, 1048583)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 8)-net over F3, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, using
- net from sequence [i] based on digital (2, 7)-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 (2, 10, 8)-net over F3, using
(161−16, 161, 2796209)-Net over F3 — Digital
Digital (145, 161, 2796209)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3161, 2796209, F3, 3, 16) (dual of [(2796209, 3), 8388466, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(310, 8, F3, 3, 8) (dual of [(8, 3), 14, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,15P) [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, 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(310, 8, F3, 3, 8) (dual of [(8, 3), 14, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(161−16, 161, large)-Net in Base 3 — Upper bound on s
There is no (145, 161, large)-net in base 3, because
- 14 times m-reduction [i] would yield (145, 147, large)-net in base 3, but