Best Known (145−25, 145, s)-Nets in Base 3
(145−25, 145, 1640)-Net over F3 — Constructive and digital
Digital (120, 145, 1640)-net over F3, using
- net defined by OOA [i] based on linear OOA(3145, 1640, F3, 25, 25) (dual of [(1640, 25), 40855, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3145, 19681, F3, 25) (dual of [19681, 19536, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3145, 19681, F3, 25) (dual of [19681, 19536, 26]-code), using
(145−25, 145, 6561)-Net over F3 — Digital
Digital (120, 145, 6561)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3145, 6561, F3, 3, 25) (dual of [(6561, 3), 19538, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- OOA 3-folding [i] based on linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using
(145−25, 145, 1405344)-Net in Base 3 — Upper bound on s
There is no (120, 145, 1405345)-net in base 3, because
- 1 times m-reduction [i] would yield (120, 144, 1405345)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 507 529235 291531 140453 883465 401623 617676 504056 106925 594414 725922 149617 > 3144 [i]