Best Known (3, 3+5, s)-Nets in Base 128
(3, 3+5, 8128)-Net over F128 — Constructive and digital
Digital (3, 8, 8128)-net over F128, using
- 1281 times duplication [i] based on digital (2, 7, 8128)-net over F128, using
- net defined by OOA [i] based on linear OOA(1287, 8128, F128, 5, 5) (dual of [(8128, 5), 40633, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(1287, 8128, F128, 4, 5) (dual of [(8128, 4), 32505, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(1287, 16257, F128, 5) (dual of [16257, 16250, 6]-code), using
- appending kth column [i] based on linear OOA(1287, 8128, F128, 4, 5) (dual of [(8128, 4), 32505, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1287, 8128, F128, 5, 5) (dual of [(8128, 5), 40633, 6]-NRT-code), using
(3, 3+5, 8129)-Net over F128 — Digital
Digital (3, 8, 8129)-net over F128, using
- net defined by OOA [i] based on linear OOA(1288, 8129, F128, 5, 5) (dual of [(8129, 5), 40637, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(1288, 8129, F128, 4, 5) (dual of [(8129, 4), 32508, 6]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(1288, 8129, F128, 2, 5) (dual of [(8129, 2), 16250, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1288, 16258, F128, 5) (dual of [16258, 16250, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(1287, 16257, F128, 5) (dual of [16257, 16250, 6]-code), using
- OOA 2-folding [i] based on linear OA(1288, 16258, F128, 5) (dual of [16258, 16250, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(1288, 8129, F128, 2, 5) (dual of [(8129, 2), 16250, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(1288, 8129, F128, 4, 5) (dual of [(8129, 4), 32508, 6]-NRT-code), using
(3, 3+5, 32640)-Net in Base 128 — Constructive
(3, 8, 32640)-net in base 128, using
- base change [i] based on digital (2, 7, 32640)-net over F256, using
- net defined by OOA [i] based on linear OOA(2567, 32640, F256, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- net defined by OOA [i] based on linear OOA(2567, 32640, F256, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
(3, 3+5, 264207)-Net in Base 128 — Upper bound on s
There is no (3, 8, 264208)-net in base 128, because
- 1 times m-reduction [i] would yield (3, 7, 264208)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 562 951614 364777 > 1287 [i]