Best Known (35, 45, s)-Nets in Base 16
(35, 45, 26335)-Net over F16 — Constructive and digital
Digital (35, 45, 26335)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 120)-net over F16, using
- net defined by OOA [i] based on linear OOA(167, 120, F16, 5, 5) (dual of [(120, 5), 593, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- net defined by OOA [i] based on linear OOA(167, 120, F16, 5, 5) (dual of [(120, 5), 593, 6]-NRT-code), using
- digital (28, 38, 26215)-net over F16, using
- net defined by OOA [i] based on linear OOA(1638, 26215, F16, 10, 10) (dual of [(26215, 10), 262112, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(1638, 131075, F16, 10) (dual of [131075, 131037, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(1638, 131076, F16, 10) (dual of [131076, 131038, 11]-code), using
- trace code [i] based on linear OA(25619, 65538, F256, 10) (dual of [65538, 65519, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- 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(25617, 65536, F256, 9) (dual of [65536, 65519, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [i] based on
- trace code [i] based on linear OA(25619, 65538, F256, 10) (dual of [65538, 65519, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(1638, 131076, F16, 10) (dual of [131076, 131038, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(1638, 131075, F16, 10) (dual of [131075, 131037, 11]-code), using
- net defined by OOA [i] based on linear OOA(1638, 26215, F16, 10, 10) (dual of [(26215, 10), 262112, 11]-NRT-code), using
- digital (2, 7, 120)-net over F16, using
(35, 45, 52431)-Net in Base 16 — Constructive
(35, 45, 52431)-net in base 16, using
- base change [i] based on digital (20, 30, 52431)-net over F64, using
- net defined by OOA [i] based on linear OOA(6430, 52431, F64, 10, 10) (dual of [(52431, 10), 524280, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(6430, 262155, F64, 10) (dual of [262155, 262125, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- 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(6419, 262144, F64, 7) (dual of [262144, 262125, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- OA 5-folding and stacking [i] based on linear OA(6430, 262155, F64, 10) (dual of [262155, 262125, 11]-code), using
- net defined by OOA [i] based on linear OOA(6430, 52431, F64, 10, 10) (dual of [(52431, 10), 524280, 11]-NRT-code), using
(35, 45, 289912)-Net over F16 — Digital
Digital (35, 45, 289912)-net over F16, using
(35, 45, large)-Net in Base 16 — Upper bound on s
There is no (35, 45, large)-net in base 16, because
- 8 times m-reduction [i] would yield (35, 37, large)-net in base 16, but