Best Known (53, 53+38, s)-Nets in Base 64
(53, 53+38, 641)-Net over F64 — Constructive and digital
Digital (53, 91, 641)-net over F64, using
- t-expansion [i] based on digital (52, 91, 641)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (5, 24, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- digital (28, 67, 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 (5, 24, 128)-net over F64, using
- (u, u+v)-construction [i] based on
(53, 53+38, 862)-Net in Base 64 — Constructive
(53, 91, 862)-net in base 64, using
- t-expansion [i] based on (52, 91, 862)-net in base 64, using
- base change [i] based on digital (39, 78, 862)-net over F128, using
- 1281 times duplication [i] based on digital (38, 77, 862)-net over F128, using
- net defined by OOA [i] based on linear OOA(12877, 862, F128, 39, 39) (dual of [(862, 39), 33541, 40]-NRT-code), using
- OOA 19-folding and stacking with additional row [i] based on linear OA(12877, 16379, F128, 39) (dual of [16379, 16302, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(12877, 16384, F128, 39) (dual of [16384, 16307, 40]-code), using
- an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- discarding factors / shortening the dual code based on linear OA(12877, 16384, F128, 39) (dual of [16384, 16307, 40]-code), using
- OOA 19-folding and stacking with additional row [i] based on linear OA(12877, 16379, F128, 39) (dual of [16379, 16302, 40]-code), using
- net defined by OOA [i] based on linear OOA(12877, 862, F128, 39, 39) (dual of [(862, 39), 33541, 40]-NRT-code), using
- 1281 times duplication [i] based on digital (38, 77, 862)-net over F128, using
- base change [i] based on digital (39, 78, 862)-net over F128, using
(53, 53+38, 6457)-Net over F64 — Digital
Digital (53, 91, 6457)-net over F64, using
(53, 53+38, large)-Net in Base 64 — Upper bound on s
There is no (53, 91, large)-net in base 64, because
- 36 times m-reduction [i] would yield (53, 55, large)-net in base 64, but