Best Known (47−11, 47, s)-Nets in Base 16
(47−11, 47, 26232)-Net over F16 — Constructive and digital
Digital (36, 47, 26232)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (31, 42, 26215)-net over F16, using
- net defined by OOA [i] based on linear OOA(1642, 26215, F16, 11, 11) (dual of [(26215, 11), 288323, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(1642, 131076, F16, 11) (dual of [131076, 131034, 12]-code), using
- trace code [i] based on linear OA(25621, 65538, F256, 11) (dual of [65538, 65517, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- trace code [i] based on linear OA(25621, 65538, F256, 11) (dual of [65538, 65517, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(1642, 131076, F16, 11) (dual of [131076, 131034, 12]-code), using
- net defined by OOA [i] based on linear OOA(1642, 26215, F16, 11, 11) (dual of [(26215, 11), 288323, 12]-NRT-code), using
- digital (0, 5, 17)-net over F16, using
(47−11, 47, 52429)-Net in Base 16 — Constructive
(36, 47, 52429)-net in base 16, using
- net defined by OOA [i] based on OOA(1647, 52429, S16, 11, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(1647, 262146, S16, 11), using
- discarding factors based on OA(1647, 262147, S16, 11), using
- discarding parts of the base [i] based on linear OA(6431, 262147, F64, 11) (dual of [262147, 262116, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(6428, 262144, F64, 10) (dual of [262144, 262116, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- discarding parts of the base [i] based on linear OA(6431, 262147, F64, 11) (dual of [262147, 262116, 12]-code), using
- discarding factors based on OA(1647, 262147, S16, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(1647, 262146, S16, 11), using
(47−11, 47, 137805)-Net over F16 — Digital
Digital (36, 47, 137805)-net over F16, using
(47−11, 47, large)-Net in Base 16 — Upper bound on s
There is no (36, 47, large)-net in base 16, because
- 9 times m-reduction [i] would yield (36, 38, large)-net in base 16, but