Best Known (2, 6, s)-Nets in Base 8
(2, 6, 28)-Net over F8 — Constructive and digital
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
(2, 6, 36)-Net over F8 — Digital
Digital (2, 6, 36)-net over F8, using
- net defined by OOA [i] based on linear OOA(86, 36, F8, 4, 4) (dual of [(36, 4), 138, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(86, 36, F8, 3, 4) (dual of [(36, 3), 102, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(86, 36, F8, 4) (dual of [36, 30, 5]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(86, 36, F8, 4) (dual of [36, 30, 5]-code), using
- appending kth column [i] based on linear OOA(86, 36, F8, 3, 4) (dual of [(36, 3), 102, 5]-NRT-code), using
(2, 6, 101)-Net in Base 8 — Upper bound on s
There is no (2, 6, 102)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(86, 102, S8, 4), but
- the linear programming bound shows that M ≥ 125 579264 / 475 > 86 [i]