Best Known (87−28, 87, s)-Nets in Base 64
(87−28, 87, 18726)-Net over F64 — Constructive and digital
Digital (59, 87, 18726)-net over F64, using
- net defined by OOA [i] based on linear OOA(6487, 18726, F64, 28, 28) (dual of [(18726, 28), 524241, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(6487, 262164, F64, 28) (dual of [262164, 262077, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(6487, 262167, F64, 28) (dual of [262167, 262080, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(645, 23, F64, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(6487, 262167, F64, 28) (dual of [262167, 262080, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(6487, 262164, F64, 28) (dual of [262164, 262077, 29]-code), using
(87−28, 87, 157836)-Net over F64 — Digital
Digital (59, 87, 157836)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6487, 157836, F64, 28) (dual of [157836, 157749, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(6487, 262167, F64, 28) (dual of [262167, 262080, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(645, 23, F64, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(6487, 262167, F64, 28) (dual of [262167, 262080, 29]-code), using
(87−28, 87, large)-Net in Base 64 — Upper bound on s
There is no (59, 87, large)-net in base 64, because
- 26 times m-reduction [i] would yield (59, 61, large)-net in base 64, but