Best Known (115−20, 115, s)-Nets in Base 16
(115−20, 115, 838860)-Net over F16 — Constructive and digital
Digital (95, 115, 838860)-net over F16, using
- t-expansion [i] based on digital (94, 115, 838860)-net over F16, using
- net defined by OOA [i] based on linear OOA(16115, 838860, F16, 21, 21) (dual of [(838860, 21), 17615945, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(16115, 8388601, F16, 21) (dual of [8388601, 8388486, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(16115, large, F16, 21) (dual of [large, large−115, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(16115, large, F16, 21) (dual of [large, large−115, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(16115, 8388601, F16, 21) (dual of [8388601, 8388486, 22]-code), using
- net defined by OOA [i] based on linear OOA(16115, 838860, F16, 21, 21) (dual of [(838860, 21), 17615945, 22]-NRT-code), using
(115−20, 115, large)-Net over F16 — Digital
Digital (95, 115, large)-net over F16, using
- t-expansion [i] based on digital (94, 115, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16115, large, F16, 21) (dual of [large, large−115, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16115, large, F16, 21) (dual of [large, large−115, 22]-code), using
(115−20, 115, large)-Net in Base 16 — Upper bound on s
There is no (95, 115, large)-net in base 16, because
- 18 times m-reduction [i] would yield (95, 97, large)-net in base 16, but