Best Known (105, 105+16, s)-Nets in Base 3
(105, 105+16, 66430)-Net over F3 — Constructive and digital
Digital (105, 121, 66430)-net over F3, using
- net defined by OOA [i] based on linear OOA(3121, 66430, F3, 16, 16) (dual of [(66430, 16), 1062759, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3121, 531440, F3, 16) (dual of [531440, 531319, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3121, 531440, F3, 16) (dual of [531440, 531319, 17]-code), using
(105, 105+16, 132860)-Net over F3 — Digital
Digital (105, 121, 132860)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3121, 132860, F3, 4, 16) (dual of [(132860, 4), 531319, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3121, 531440, F3, 16) (dual of [531440, 531319, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using
- OOA 4-folding [i] based on linear OA(3121, 531440, F3, 16) (dual of [531440, 531319, 17]-code), using
(105, 105+16, large)-Net in Base 3 — Upper bound on s
There is no (105, 121, large)-net in base 3, because
- 14 times m-reduction [i] would yield (105, 107, large)-net in base 3, but