Best Known (88−39, 88, s)-Nets in Base 64
(88−39, 88, 593)-Net over F64 — Constructive and digital
Digital (49, 88, 593)-net over F64, using
- 1 times m-reduction [i] based on digital (49, 89, 593)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 21, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (28, 68, 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
- digital (1, 21, 80)-net over F64, using
- (u, u+v)-construction [i] based on
(88−39, 88, 4089)-Net over F64 — Digital
Digital (49, 88, 4089)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6488, 4089, F64, 39) (dual of [4089, 4001, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(6488, 4132, F64, 39) (dual of [4132, 4044, 40]-code), using
- construction X applied to C([0,19]) ⊂ C([0,13]) [i] based on
- linear OA(6477, 4097, F64, 39) (dual of [4097, 4020, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(6453, 4097, F64, 27) (dual of [4097, 4044, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(6411, 35, F64, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,64)), using
- discarding factors / shortening the dual code based on linear OA(6411, 64, F64, 11) (dual of [64, 53, 12]-code or 64-arc in PG(10,64)), using
- Reed–Solomon code RS(53,64) [i]
- discarding factors / shortening the dual code based on linear OA(6411, 64, F64, 11) (dual of [64, 53, 12]-code or 64-arc in PG(10,64)), using
- construction X applied to C([0,19]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6488, 4132, F64, 39) (dual of [4132, 4044, 40]-code), using
(88−39, 88, large)-Net in Base 64 — Upper bound on s
There is no (49, 88, large)-net in base 64, because
- 37 times m-reduction [i] would yield (49, 51, large)-net in base 64, but