Best Known (33, 42, s)-Nets in Base 8
(33, 42, 8219)-Net over F8 — Constructive and digital
Digital (33, 42, 8219)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 28)-net over F8, using
- net defined by OOA [i] based on linear OOA(86, 28, F8, 4, 4) (dual of [(28, 4), 106, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(86, 28, F8, 3, 4) (dual of [(28, 3), 78, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- appending kth column [i] based on linear OOA(86, 28, F8, 3, 4) (dual of [(28, 3), 78, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(86, 28, F8, 4, 4) (dual of [(28, 4), 106, 5]-NRT-code), using
- digital (27, 36, 8191)-net over F8, using
- net defined by OOA [i] based on linear OOA(836, 8191, F8, 9, 9) (dual of [(8191, 9), 73683, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(836, 32765, F8, 9) (dual of [32765, 32729, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(836, 32765, F8, 9) (dual of [32765, 32729, 10]-code), using
- net defined by OOA [i] based on linear OOA(836, 8191, F8, 9, 9) (dual of [(8191, 9), 73683, 10]-NRT-code), using
- digital (2, 6, 28)-net over F8, using
(33, 42, 32826)-Net over F8 — Digital
Digital (33, 42, 32826)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(842, 32826, F8, 9) (dual of [32826, 32784, 10]-code), using
- (u, u+v)-construction [i] based on
- linear OA(86, 58, F8, 4) (dual of [58, 52, 5]-code), using
- a “Gra†code from Grassl’s database [i]
- linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(86, 58, F8, 4) (dual of [58, 52, 5]-code), using
- (u, u+v)-construction [i] based on
(33, 42, large)-Net in Base 8 — Upper bound on s
There is no (33, 42, large)-net in base 8, because
- 7 times m-reduction [i] would yield (33, 35, large)-net in base 8, but