Best Known (20, 20+16, s)-Nets in Base 64
(20, 20+16, 514)-Net over F64 — Constructive and digital
Digital (20, 36, 514)-net over F64, using
- net defined by OOA [i] based on linear OOA(6436, 514, F64, 16, 16) (dual of [(514, 16), 8188, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(6436, 4112, F64, 16) (dual of [4112, 4076, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6436, 4113, F64, 16) (dual of [4113, 4077, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(645, 17, F64, 5) (dual of [17, 12, 6]-code or 17-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(15) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(6436, 4113, F64, 16) (dual of [4113, 4077, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(6436, 4112, F64, 16) (dual of [4112, 4076, 17]-code), using
(20, 20+16, 517)-Net in Base 64 — Constructive
(20, 36, 517)-net in base 64, using
- base change [i] based on digital (11, 27, 517)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (2, 18, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (1, 9, 258)-net over F256, using
- (u, u+v)-construction [i] based on
(20, 20+16, 3138)-Net over F64 — Digital
Digital (20, 36, 3138)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6436, 3138, F64, 16) (dual of [3138, 3102, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6436, 4113, F64, 16) (dual of [4113, 4077, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(645, 17, F64, 5) (dual of [17, 12, 6]-code or 17-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(15) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(6436, 4113, F64, 16) (dual of [4113, 4077, 17]-code), using
(20, 20+16, 8019719)-Net in Base 64 — Upper bound on s
There is no (20, 36, 8019720)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 105312 297737 015545 414403 703698 054029 689175 418789 417959 400234 979808 > 6436 [i]