Best Known (27, 36, s)-Nets in Base 64
(27, 36, 2097150)-Net over F64 — Constructive and digital
Digital (27, 36, 2097150)-net over F64, using
- 643 times duplication [i] based on 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
(27, 36, large)-Net over F64 — Digital
Digital (27, 36, large)-net over F64, using
- 643 times duplication [i] based on digital (24, 33, large)-net over F64, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] 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]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6433, large, F64, 9) (dual of [large, large−33, 10]-code), using
(27, 36, large)-Net in Base 64 — Upper bound on s
There is no (27, 36, large)-net in base 64, because
- 7 times m-reduction [i] would yield (27, 29, large)-net in base 64, but