Best Known (47−9, 47, s)-Nets in Base 3
(47−9, 47, 819)-Net over F3 — Constructive and digital
Digital (38, 47, 819)-net over F3, using
- net defined by OOA [i] based on linear OOA(347, 819, F3, 9, 9) (dual of [(819, 9), 7324, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(347, 3277, F3, 9) (dual of [3277, 3230, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(347, 3280, F3, 9) (dual of [3280, 3233, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(347, 3277, F3, 9) (dual of [3277, 3230, 10]-code), using
(47−9, 47, 2302)-Net over F3 — Digital
Digital (38, 47, 2302)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(347, 2302, F3, 9) (dual of [2302, 2255, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(347, 3280, F3, 9) (dual of [3280, 3233, 10]-code), using
(47−9, 47, 339557)-Net in Base 3 — Upper bound on s
There is no (38, 47, 339558)-net in base 3, because
- 1 times m-reduction [i] would yield (38, 46, 339558)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 8863 036022 648297 834249 > 346 [i]