Best Known (34, 42, s)-Nets in Base 8
(34, 42, 65535)-Net over F8 — Constructive and digital
Digital (34, 42, 65535)-net over F8, using
- net defined by OOA [i] based on linear OOA(842, 65535, F8, 8, 8) (dual of [(65535, 8), 524238, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(842, 262140, F8, 8) (dual of [262140, 262098, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(842, 262143, F8, 8) (dual of [262143, 262101, 9]-code), using
- 1 times truncation [i] based on linear OA(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 1 times truncation [i] based on linear OA(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(842, 262143, F8, 8) (dual of [262143, 262101, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(842, 262140, F8, 8) (dual of [262140, 262098, 9]-code), using
(34, 42, 262143)-Net over F8 — Digital
Digital (34, 42, 262143)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(842, 262143, F8, 8) (dual of [262143, 262101, 9]-code), using
- 1 times truncation [i] based on linear OA(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 1 times truncation [i] based on linear OA(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using
(34, 42, large)-Net in Base 8 — Upper bound on s
There is no (34, 42, large)-net in base 8, because
- 6 times m-reduction [i] would yield (34, 36, large)-net in base 8, but