Best Known (126, 126+27, s)-Nets in Base 8
(126, 126+27, 20179)-Net over F8 — Constructive and digital
Digital (126, 153, 20179)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (1, 14, 14)-net over F8, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- a shift-net [i]
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- digital (112, 139, 20165)-net over F8, using
- net defined by OOA [i] based on linear OOA(8139, 20165, F8, 27, 27) (dual of [(20165, 27), 544316, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8139, 262146, F8, 27) (dual of [262146, 262007, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8139, 262150, F8, 27) (dual of [262150, 262011, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(8139, 262144, F8, 27) (dual of [262144, 262005, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8133, 262144, F8, 26) (dual of [262144, 262011, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(80, 6, F8, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(8139, 262150, F8, 27) (dual of [262150, 262011, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8139, 262146, F8, 27) (dual of [262146, 262007, 28]-code), using
- net defined by OOA [i] based on linear OOA(8139, 20165, F8, 27, 27) (dual of [(20165, 27), 544316, 28]-NRT-code), using
- digital (1, 14, 14)-net over F8, using
(126, 126+27, 310850)-Net over F8 — Digital
Digital (126, 153, 310850)-net over F8, using
(126, 126+27, large)-Net in Base 8 — Upper bound on s
There is no (126, 153, large)-net in base 8, because
- 25 times m-reduction [i] would yield (126, 128, large)-net in base 8, but