Best Known (93, 93+34, s)-Nets in Base 16
(93, 93+34, 3855)-Net over F16 — Constructive and digital
Digital (93, 127, 3855)-net over F16, using
- 162 times duplication [i] based on digital (91, 125, 3855)-net over F16, using
- net defined by OOA [i] based on linear OOA(16125, 3855, F16, 34, 34) (dual of [(3855, 34), 130945, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(16125, 65535, F16, 34) (dual of [65535, 65410, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(16125, 65535, F16, 34) (dual of [65535, 65410, 35]-code), using
- net defined by OOA [i] based on linear OOA(16125, 3855, F16, 34, 34) (dual of [(3855, 34), 130945, 35]-NRT-code), using
(93, 93+34, 46974)-Net over F16 — Digital
Digital (93, 127, 46974)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16127, 46974, F16, 34) (dual of [46974, 46847, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(16127, 65546, F16, 34) (dual of [65546, 65419, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(16117, 65536, F16, 31) (dual of [65536, 65419, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(162, 10, F16, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(16127, 65546, F16, 34) (dual of [65546, 65419, 35]-code), using
(93, 93+34, large)-Net in Base 16 — Upper bound on s
There is no (93, 127, large)-net in base 16, because
- 32 times m-reduction [i] would yield (93, 95, large)-net in base 16, but