Best Known (71−12, 71, s)-Nets in Base 3
(71−12, 71, 1640)-Net over F3 — Constructive and digital
Digital (59, 71, 1640)-net over F3, using
- net defined by OOA [i] based on linear OOA(371, 1640, F3, 12, 12) (dual of [(1640, 12), 19609, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(371, 9840, F3, 12) (dual of [9840, 9769, 13]-code), using
(71−12, 71, 4943)-Net over F3 — Digital
Digital (59, 71, 4943)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(371, 4943, F3, 12) (dual of [4943, 4872, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(371, 9840, F3, 12) (dual of [9840, 9769, 13]-code), using
(71−12, 71, 662404)-Net in Base 3 — Upper bound on s
There is no (59, 71, 662405)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 7509 494870 786224 525052 437191 954753 > 371 [i]