Best Known (37−11, 37, s)-Nets in Base 64
(37−11, 37, 52509)-Net over F64 — Constructive and digital
Digital (26, 37, 52509)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 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 (20, 31, 52429)-net over F64, using
- net defined by OOA [i] based on linear OOA(6431, 52429, F64, 11, 11) (dual of [(52429, 11), 576688, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6431, 262146, F64, 11) (dual of [262146, 262115, 12]-code), using
- discarding factors / shortening the dual code 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 factors / shortening the dual code based on linear OA(6431, 262147, F64, 11) (dual of [262147, 262116, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6431, 262146, F64, 11) (dual of [262146, 262115, 12]-code), using
- net defined by OOA [i] based on linear OOA(6431, 52429, F64, 11, 11) (dual of [(52429, 11), 576688, 12]-NRT-code), using
- digital (1, 6, 80)-net over F64, using
(37−11, 37, 346344)-Net over F64 — Digital
Digital (26, 37, 346344)-net over F64, using
(37−11, 37, 419430)-Net in Base 64 — Constructive
(26, 37, 419430)-net in base 64, using
- net defined by OOA [i] based on OOA(6437, 419430, S64, 11, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(6437, 2097151, S64, 11), using
- discarding factors based on OA(6437, 2097155, S64, 11), using
- discarding parts of the base [i] based on linear OA(12831, 2097155, F128, 11) (dual of [2097155, 2097124, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 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(12831, 2097155, F128, 11) (dual of [2097155, 2097124, 12]-code), using
- discarding factors based on OA(6437, 2097155, S64, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(6437, 2097151, S64, 11), using
(37−11, 37, 524288)-Net in Base 64
(26, 37, 524288)-net in base 64, using
- net defined by OOA [i] based on OOA(6437, 524288, S64, 15, 11), using
- OOA 2-folding and stacking with additional row [i] based on OOA(6437, 1048577, S64, 3, 11), using
- discarding parts of the base [i] based on linear OOA(12831, 1048577, F128, 3, 11) (dual of [(1048577, 3), 3145700, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12831, 1048577, F128, 2, 11) (dual of [(1048577, 2), 2097123, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12831, 2097154, F128, 11) (dual of [2097154, 2097123, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(12831, 2097155, F128, 11) (dual of [2097155, 2097124, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(12831, 2097155, F128, 11) (dual of [2097155, 2097124, 12]-code), using
- OOA 2-folding [i] based on linear OA(12831, 2097154, F128, 11) (dual of [2097154, 2097123, 12]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12831, 1048577, F128, 2, 11) (dual of [(1048577, 2), 2097123, 12]-NRT-code), using
- discarding parts of the base [i] based on linear OOA(12831, 1048577, F128, 3, 11) (dual of [(1048577, 3), 3145700, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on OOA(6437, 1048577, S64, 3, 11), using
(37−11, 37, large)-Net in Base 64 — Upper bound on s
There is no (26, 37, large)-net in base 64, because
- 9 times m-reduction [i] would yield (26, 28, large)-net in base 64, but