Best Known (98, 98+24, s)-Nets in Base 16
(98, 98+24, 87385)-Net over F16 — Constructive and digital
Digital (98, 122, 87385)-net over F16, using
- 161 times duplication [i] based on digital (97, 121, 87385)-net over F16, using
- net defined by OOA [i] based on linear OOA(16121, 87385, F16, 24, 24) (dual of [(87385, 24), 2097119, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(16121, 1048620, F16, 24) (dual of [1048620, 1048499, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(16121, 1048621, F16, 24) (dual of [1048621, 1048500, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- linear OA(16111, 1048576, F16, 24) (dual of [1048576, 1048465, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(1610, 45, F16, 6) (dual of [45, 35, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(1610, 85, F16, 6) (dual of [85, 75, 7]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(16121, 1048621, F16, 24) (dual of [1048621, 1048500, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(16121, 1048620, F16, 24) (dual of [1048620, 1048499, 25]-code), using
- net defined by OOA [i] based on linear OOA(16121, 87385, F16, 24, 24) (dual of [(87385, 24), 2097119, 25]-NRT-code), using
(98, 98+24, 1532638)-Net over F16 — Digital
Digital (98, 122, 1532638)-net over F16, using
(98, 98+24, large)-Net in Base 16 — Upper bound on s
There is no (98, 122, large)-net in base 16, because
- 22 times m-reduction [i] would yield (98, 100, large)-net in base 16, but