Best Known (36−12, 36, s)-Nets in Base 64
(36−12, 36, 43692)-Net over F64 — Constructive and digital
Digital (24, 36, 43692)-net over F64, using
- net defined by OOA [i] based on linear OOA(6436, 43692, F64, 12, 12) (dual of [(43692, 12), 524268, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(6436, 262152, F64, 12) (dual of [262152, 262116, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6436, 262155, F64, 12) (dual of [262155, 262119, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6425, 262144, F64, 9) (dual of [262144, 262119, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(6436, 262155, F64, 12) (dual of [262155, 262119, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(6436, 262152, F64, 12) (dual of [262152, 262116, 13]-code), using
(36−12, 36, 150749)-Net over F64 — Digital
Digital (24, 36, 150749)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6436, 150749, F64, 12) (dual of [150749, 150713, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6436, 262155, F64, 12) (dual of [262155, 262119, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6425, 262144, F64, 9) (dual of [262144, 262119, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(6436, 262155, F64, 12) (dual of [262155, 262119, 13]-code), using
(36−12, 36, large)-Net in Base 64 — Upper bound on s
There is no (24, 36, large)-net in base 64, because
- 10 times m-reduction [i] would yield (24, 26, large)-net in base 64, but