Best Known (30, 30+9, s)-Nets in Base 64
(30, 30+9, 2099166)-Net over F64 — Constructive and digital
Digital (30, 39, 2099166)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 2016)-net over F64, using
- net defined by OOA [i] based on linear OOA(646, 2016, F64, 4, 4) (dual of [(2016, 4), 8058, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(646, 2016, F64, 3, 4) (dual of [(2016, 3), 6042, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- 1 times truncation [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- appending kth column [i] based on linear OOA(646, 2016, F64, 3, 4) (dual of [(2016, 3), 6042, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(646, 2016, F64, 4, 4) (dual of [(2016, 4), 8058, 5]-NRT-code), using
- digital (24, 33, 2097150)-net over F64, using
- net defined by OOA [i] based on linear OOA(6433, 2097150, F64, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(6433, 8388601, F64, 9) (dual of [8388601, 8388568, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(6433, large, F64, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6433, large, F64, 9) (dual of [large, large−33, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(6433, 8388601, F64, 9) (dual of [8388601, 8388568, 10]-code), using
- net defined by OOA [i] based on linear OOA(6433, 2097150, F64, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
- digital (2, 6, 2016)-net over F64, using
(30, 30+9, large)-Net over F64 — Digital
Digital (30, 39, large)-net over F64, using
- 641 times duplication [i] based on digital (29, 38, large)-net over F64, using
- t-expansion [i] based on digital (28, 38, large)-net over F64, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6438, large, F64, 10) (dual of [large, large−38, 11]-code), using
- 1 times code embedding in larger space [i] based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 1 times code embedding in larger space [i] based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6438, large, F64, 10) (dual of [large, large−38, 11]-code), using
- t-expansion [i] based on digital (28, 38, large)-net over F64, using
(30, 30+9, large)-Net in Base 64 — Upper bound on s
There is no (30, 39, large)-net in base 64, because
- 7 times m-reduction [i] would yield (30, 32, large)-net in base 64, but