Best Known (93, 93+23, s)-Nets in Base 16
(93, 93+23, 95328)-Net over F16 — Constructive and digital
Digital (93, 116, 95328)-net over F16, using
- 163 times duplication [i] based on digital (90, 113, 95328)-net over F16, using
- net defined by OOA [i] based on linear OOA(16113, 95328, F16, 23, 23) (dual of [(95328, 23), 2192431, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(16113, 1048609, F16, 23) (dual of [1048609, 1048496, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(16113, 1048613, F16, 23) (dual of [1048613, 1048500, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(167, 37, F16, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(16113, 1048613, F16, 23) (dual of [1048613, 1048500, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(16113, 1048609, F16, 23) (dual of [1048609, 1048496, 24]-code), using
- net defined by OOA [i] based on linear OOA(16113, 95328, F16, 23, 23) (dual of [(95328, 23), 2192431, 24]-NRT-code), using
(93, 93+23, 1348222)-Net over F16 — Digital
Digital (93, 116, 1348222)-net over F16, using
(93, 93+23, large)-Net in Base 16 — Upper bound on s
There is no (93, 116, large)-net in base 16, because
- 21 times m-reduction [i] would yield (93, 95, large)-net in base 16, but