Best Known (35−11, 35, s)-Nets in Base 64
(35−11, 35, 52432)-Net over F64 — Constructive and digital
Digital (24, 35, 52432)-net over F64, using
- net defined by OOA [i] based on linear OOA(6435, 52432, F64, 11, 11) (dual of [(52432, 11), 576717, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6435, 262161, F64, 11) (dual of [262161, 262126, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(6435, 262163, F64, 11) (dual of [262163, 262128, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
- linear OA(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(644, 19, F64, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(6435, 262163, F64, 11) (dual of [262163, 262128, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6435, 262161, F64, 11) (dual of [262161, 262126, 12]-code), using
(35−11, 35, 262163)-Net over F64 — Digital
Digital (24, 35, 262163)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6435, 262163, F64, 11) (dual of [262163, 262128, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
- linear OA(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(644, 19, F64, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
(35−11, 35, large)-Net in Base 64 — Upper bound on s
There is no (24, 35, large)-net in base 64, because
- 9 times m-reduction [i] would yield (24, 26, large)-net in base 64, but