Best Known (103−16, 103, s)-Nets in Base 8
(103−16, 103, 262148)-Net over F8 — Constructive and digital
Digital (87, 103, 262148)-net over F8, using
- net defined by OOA [i] based on linear OOA(8103, 262148, F8, 16, 16) (dual of [(262148, 16), 4194265, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(8103, 2097184, F8, 16) (dual of [2097184, 2097081, 17]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- OA 8-folding and stacking [i] based on linear OA(8103, 2097184, F8, 16) (dual of [2097184, 2097081, 17]-code), using
(103−16, 103, 2097184)-Net over F8 — Digital
Digital (87, 103, 2097184)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8103, 2097184, F8, 16) (dual of [2097184, 2097081, 17]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
(103−16, 103, large)-Net in Base 8 — Upper bound on s
There is no (87, 103, large)-net in base 8, because
- 14 times m-reduction [i] would yield (87, 89, large)-net in base 8, but