Best Known (100, 130, s)-Nets in Base 16
(100, 130, 8740)-Net over F16 — Constructive and digital
Digital (100, 130, 8740)-net over F16, using
- 164 times duplication [i] based on digital (96, 126, 8740)-net over F16, using
- net defined by OOA [i] based on linear OOA(16126, 8740, F16, 30, 30) (dual of [(8740, 30), 262074, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(16126, 131100, F16, 30) (dual of [131100, 130974, 31]-code), using
- trace code [i] based on linear OA(25663, 65550, F256, 30) (dual of [65550, 65487, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- trace code [i] based on linear OA(25663, 65550, F256, 30) (dual of [65550, 65487, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(16126, 131100, F16, 30) (dual of [131100, 130974, 31]-code), using
- net defined by OOA [i] based on linear OOA(16126, 8740, F16, 30, 30) (dual of [(8740, 30), 262074, 31]-NRT-code), using
(100, 130, 194465)-Net over F16 — Digital
Digital (100, 130, 194465)-net over F16, using
(100, 130, large)-Net in Base 16 — Upper bound on s
There is no (100, 130, large)-net in base 16, because
- 28 times m-reduction [i] would yield (100, 102, large)-net in base 16, but