Best Known (39, 70, s)-Nets in Base 64
(39, 70, 513)-Net over F64 — Constructive and digital
Digital (39, 70, 513)-net over F64, using
- t-expansion [i] based on digital (28, 70, 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
(39, 70, 547)-Net in Base 64 — Constructive
(39, 70, 547)-net in base 64, using
- (u, u+v)-construction [i] based on
- (8, 23, 259)-net in base 64, using
- 1 times m-reduction [i] based on (8, 24, 259)-net in base 64, using
- base change [i] based on digital (2, 18, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 18, 259)-net over F256, using
- 1 times m-reduction [i] based on (8, 24, 259)-net in base 64, using
- (16, 47, 288)-net in base 64, using
- 2 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
- base change [i] based on digital (9, 42, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 42, 288)-net over F128, using
- 2 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
- (8, 23, 259)-net in base 64, using
(39, 70, 3661)-Net over F64 — Digital
Digital (39, 70, 3661)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6470, 3661, F64, 31) (dual of [3661, 3591, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(6470, 4126, F64, 31) (dual of [4126, 4056, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,10]) [i] based on
- linear OA(6461, 4097, F64, 31) (dual of [4097, 4036, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(6441, 4097, F64, 21) (dual of [4097, 4056, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(649, 29, F64, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,64)), using
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), using
- Reed–Solomon code RS(55,64) [i]
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), using
- construction X applied to C([0,15]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6470, 4126, F64, 31) (dual of [4126, 4056, 32]-code), using
(39, 70, large)-Net in Base 64 — Upper bound on s
There is no (39, 70, large)-net in base 64, because
- 29 times m-reduction [i] would yield (39, 41, large)-net in base 64, but