Best Known (104, 104+16, s)-Nets in Base 8
(104, 104+16, 1048584)-Net over F8 — Constructive and digital
Digital (104, 120, 1048584)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (96, 112, 1048575)-net over F8, using
- net defined by OOA [i] based on linear OOA(8112, 1048575, F8, 16, 16) (dual of [(1048575, 16), 16777088, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(8112, 8388600, F8, 16) (dual of [8388600, 8388488, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(8112, large, F8, 16) (dual of [large, large−112, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(8112, large, F8, 16) (dual of [large, large−112, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(8112, 8388600, F8, 16) (dual of [8388600, 8388488, 17]-code), using
- net defined by OOA [i] based on linear OOA(8112, 1048575, F8, 16, 16) (dual of [(1048575, 16), 16777088, 17]-NRT-code), using
- digital (0, 8, 9)-net over F8, using
(104, 104+16, large)-Net over F8 — Digital
Digital (104, 120, large)-net over F8, using
- 83 times duplication [i] based on digital (101, 117, large)-net over F8, using
- t-expansion [i] based on digital (100, 117, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8117, large, F8, 17) (dual of [large, large−117, 18]-code), using
- 4 times code embedding in larger space [i] based on linear OA(8113, large, F8, 17) (dual of [large, large−113, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 4 times code embedding in larger space [i] based on linear OA(8113, large, F8, 17) (dual of [large, large−113, 18]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8117, large, F8, 17) (dual of [large, large−117, 18]-code), using
- t-expansion [i] based on digital (100, 117, large)-net over F8, using
(104, 104+16, large)-Net in Base 8 — Upper bound on s
There is no (104, 120, large)-net in base 8, because
- 14 times m-reduction [i] would yield (104, 106, large)-net in base 8, but