Best Known (54, 54+36, s)-Nets in Base 64
(54, 54+36, 690)-Net over F64 — Constructive and digital
Digital (54, 90, 690)-net over F64, using
- t-expansion [i] based on digital (53, 90, 690)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (7, 25, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- digital (28, 65, 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 (7, 25, 177)-net over F64, using
- (u, u+v)-construction [i] based on
(54, 54+36, 911)-Net in Base 64 — Constructive
(54, 90, 911)-net in base 64, using
- 1 times m-reduction [i] based on (54, 91, 911)-net in base 64, using
- base change [i] based on digital (41, 78, 911)-net over F128, using
- net defined by OOA [i] based on linear OOA(12878, 911, F128, 37, 37) (dual of [(911, 37), 33629, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(12878, 16399, F128, 37) (dual of [16399, 16321, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(12878, 16402, F128, 37) (dual of [16402, 16324, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,15]) [i] based on
- linear OA(12873, 16385, F128, 37) (dual of [16385, 16312, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(12861, 16385, F128, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(1285, 17, F128, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to C([0,18]) ⊂ C([0,15]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12878, 16402, F128, 37) (dual of [16402, 16324, 38]-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(12878, 16399, F128, 37) (dual of [16399, 16321, 38]-code), using
- net defined by OOA [i] based on linear OOA(12878, 911, F128, 37, 37) (dual of [(911, 37), 33629, 38]-NRT-code), using
- base change [i] based on digital (41, 78, 911)-net over F128, using
(54, 54+36, 9754)-Net over F64 — Digital
Digital (54, 90, 9754)-net over F64, using
(54, 54+36, large)-Net in Base 64 — Upper bound on s
There is no (54, 90, large)-net in base 64, because
- 34 times m-reduction [i] would yield (54, 56, large)-net in base 64, but