Best Known (21−5, 21, s)-Nets in Base 3
(21−5, 21, 1054)-Net over F3 — Constructive and digital
Digital (16, 21, 1054)-net over F3, using
- net defined by OOA [i] based on linear OOA(321, 1054, F3, 5, 5) (dual of [(1054, 5), 5249, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(321, 2109, F3, 5) (dual of [2109, 2088, 6]-code), using
- trace code [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(321, 2109, F3, 5) (dual of [2109, 2088, 6]-code), using
(21−5, 21, 1376)-Net over F3 — Digital
Digital (16, 21, 1376)-net over F3, using
- net defined by OOA [i] based on linear OOA(321, 1376, F3, 5, 5) (dual of [(1376, 5), 6859, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(321, 1376, F3, 4, 5) (dual of [(1376, 4), 5483, 6]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(321, 1376, F3, 5) (dual of [1376, 1355, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 2109, F3, 5) (dual of [2109, 2088, 6]-code), using
- trace code [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 2109, F3, 5) (dual of [2109, 2088, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(321, 1376, F3, 5) (dual of [1376, 1355, 6]-code), using
- appending kth column [i] based on linear OOA(321, 1376, F3, 4, 5) (dual of [(1376, 4), 5483, 6]-NRT-code), using
(21−5, 21, 41752)-Net in Base 3 — Upper bound on s
There is no (16, 21, 41753)-net in base 3, because
- 1 times m-reduction [i] would yield (16, 20, 41753)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 3486 876537 > 320 [i]