Best Known (33, 63, s)-Nets in Base 64
(33, 63, 513)-Net over F64 — Constructive and digital
Digital (33, 63, 513)-net over F64, using
- t-expansion [i] based on digital (28, 63, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(33, 63, 516)-Net in Base 64 — Constructive
(33, 63, 516)-net in base 64, using
- 1 times m-reduction [i] based on (33, 64, 516)-net in base 64, using
- base change [i] based on digital (17, 48, 516)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 16, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (1, 32, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- digital (1, 16, 258)-net over F256, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (17, 48, 516)-net over F256, using
(33, 63, 2055)-Net over F64 — Digital
Digital (33, 63, 2055)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6463, 2055, F64, 2, 30) (dual of [(2055, 2), 4047, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6463, 4110, F64, 30) (dual of [4110, 4047, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(6459, 4096, F64, 30) (dual of [4096, 4037, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(6449, 4096, F64, 25) (dual of [4096, 4047, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(644, 14, F64, 4) (dual of [14, 10, 5]-code or 14-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(29) ⊂ Ce(24) [i] based on
- OOA 2-folding [i] based on linear OA(6463, 4110, F64, 30) (dual of [4110, 4047, 31]-code), using
(33, 63, 3929897)-Net in Base 64 — Upper bound on s
There is no (33, 63, 3929898)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 615658 395125 316149 702864 105248 546168 011217 417954 884211 139477 093394 652045 054727 271851 237568 008414 320675 267674 828976 > 6463 [i]