Best Known (34, 34+18, s)-Nets in Base 64
(34, 34+18, 29127)-Net over F64 — Constructive and digital
Digital (34, 52, 29127)-net over F64, using
- net defined by OOA [i] based on linear OOA(6452, 29127, F64, 18, 18) (dual of [(29127, 18), 524234, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(6452, 262143, F64, 18) (dual of [262143, 262091, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(6452, 262143, F64, 18) (dual of [262143, 262091, 19]-code), using
(34, 34+18, 106905)-Net over F64 — Digital
Digital (34, 52, 106905)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6452, 106905, F64, 2, 18) (dual of [(106905, 2), 213758, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6452, 131073, F64, 2, 18) (dual of [(131073, 2), 262094, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6452, 262146, F64, 18) (dual of [262146, 262094, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(6452, 262147, F64, 18) (dual of [262147, 262095, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(6449, 262144, F64, 17) (dual of [262144, 262095, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(6452, 262147, F64, 18) (dual of [262147, 262095, 19]-code), using
- OOA 2-folding [i] based on linear OA(6452, 262146, F64, 18) (dual of [262146, 262094, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(6452, 131073, F64, 2, 18) (dual of [(131073, 2), 262094, 19]-NRT-code), using
(34, 34+18, large)-Net in Base 64 — Upper bound on s
There is no (34, 52, large)-net in base 64, because
- 16 times m-reduction [i] would yield (34, 36, large)-net in base 64, but