Best Known (241−37, 241, s)-Nets in Base 3
(241−37, 241, 3280)-Net over F3 — Constructive and digital
Digital (204, 241, 3280)-net over F3, using
- net defined by OOA [i] based on linear OOA(3241, 3280, F3, 37, 37) (dual of [(3280, 37), 121119, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(3241, 59041, F3, 37) (dual of [59041, 58800, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, 59049, F3, 37) (dual of [59049, 58808, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- discarding factors / shortening the dual code based on linear OA(3241, 59049, F3, 37) (dual of [59049, 58808, 38]-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(3241, 59041, F3, 37) (dual of [59041, 58800, 38]-code), using
(241−37, 241, 18139)-Net over F3 — Digital
Digital (204, 241, 18139)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3241, 18139, F3, 3, 37) (dual of [(18139, 3), 54176, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3241, 19683, F3, 3, 37) (dual of [(19683, 3), 58808, 38]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3241, 59049, F3, 37) (dual of [59049, 58808, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- OOA 3-folding [i] based on linear OA(3241, 59049, F3, 37) (dual of [59049, 58808, 38]-code), using
- discarding factors / shortening the dual code based on linear OOA(3241, 19683, F3, 3, 37) (dual of [(19683, 3), 58808, 38]-NRT-code), using
(241−37, 241, large)-Net in Base 3 — Upper bound on s
There is no (204, 241, large)-net in base 3, because
- 35 times m-reduction [i] would yield (204, 206, large)-net in base 3, but