Best Known (72−13, 72, s)-Nets in Base 3
(72−13, 72, 1640)-Net over F3 — Constructive and digital
Digital (59, 72, 1640)-net over F3, using
- net defined by OOA [i] based on linear OOA(372, 1640, F3, 13, 13) (dual of [(1640, 13), 21248, 14]-NRT-code), using
(72−13, 72, 4920)-Net over F3 — Digital
Digital (59, 72, 4920)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(372, 4920, F3, 2, 13) (dual of [(4920, 2), 9768, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(372, 9840, F3, 13) (dual of [9840, 9768, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(372, 9841, F3, 13) (dual of [9841, 9769, 14]-code), using
- OOA 2-folding [i] based on linear OA(372, 9840, F3, 13) (dual of [9840, 9768, 14]-code), using
(72−13, 72, 662404)-Net in Base 3 — Upper bound on s
There is no (59, 72, 662405)-net in base 3, because
- 1 times m-reduction [i] would yield (59, 71, 662405)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 7509 494870 786224 525052 437191 954753 > 371 [i]