Best Known (35−6, 35, s)-Nets in Base 3
(35−6, 35, 3280)-Net over F3 — Constructive and digital
Digital (29, 35, 3280)-net over F3, using
- net defined by OOA [i] based on linear OOA(335, 3280, F3, 6, 6) (dual of [(3280, 6), 19645, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(335, 3280, F3, 5, 6) (dual of [(3280, 5), 16365, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(335, 9840, F3, 6) (dual of [9840, 9805, 7]-code), using
- appending kth column [i] based on linear OOA(335, 3280, F3, 5, 6) (dual of [(3280, 5), 16365, 7]-NRT-code), using
(35−6, 35, 9840)-Net over F3 — Digital
Digital (29, 35, 9840)-net over F3, using
- net defined by OOA [i] based on linear OOA(335, 9840, F3, 6, 6) (dual of [(9840, 6), 59005, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(335, 9840, F3, 5, 6) (dual of [(9840, 5), 49165, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(335, 9840, F3, 6) (dual of [9840, 9805, 7]-code), using
- appending kth column [i] based on linear OOA(335, 9840, F3, 5, 6) (dual of [(9840, 5), 49165, 7]-NRT-code), using
(35−6, 35, 334784)-Net in Base 3 — Upper bound on s
There is no (29, 35, 334785)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 50031 835909 787931 > 335 [i]