Best Known (63−11, 63, s)-Nets in Base 3
(63−11, 63, 1968)-Net over F3 — Constructive and digital
Digital (52, 63, 1968)-net over F3, using
- net defined by OOA [i] based on linear OOA(363, 1968, F3, 11, 11) (dual of [(1968, 11), 21585, 12]-NRT-code), using
(63−11, 63, 4920)-Net over F3 — Digital
Digital (52, 63, 4920)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(363, 4920, F3, 2, 11) (dual of [(4920, 2), 9777, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(363, 9840, F3, 11) (dual of [9840, 9777, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(363, 9841, F3, 11) (dual of [9841, 9778, 12]-code), using
- OOA 2-folding [i] based on linear OA(363, 9840, F3, 11) (dual of [9840, 9777, 12]-code), using
(63−11, 63, 1074256)-Net in Base 3 — Upper bound on s
There is no (52, 63, 1074257)-net in base 3, because
- 1 times m-reduction [i] would yield (52, 62, 1074257)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 381521 300514 993294 883873 698195 > 362 [i]