Best Known (85, 85+16, s)-Nets in Base 3
(85, 85+16, 7381)-Net over F3 — Constructive and digital
Digital (85, 101, 7381)-net over F3, using
- net defined by OOA [i] based on linear OOA(3101, 7381, F3, 16, 16) (dual of [(7381, 16), 117995, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3101, 59048, F3, 16) (dual of [59048, 58947, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3101, 59048, F3, 16) (dual of [59048, 58947, 17]-code), using
(85, 85+16, 19683)-Net over F3 — Digital
Digital (85, 101, 19683)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3101, 19683, F3, 3, 16) (dual of [(19683, 3), 58948, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OOA 3-folding [i] based on linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using
(85, 85+16, 1987532)-Net in Base 3 — Upper bound on s
There is no (85, 101, 1987533)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 546134 738378 190515 178183 625551 942939 079128 635745 > 3101 [i]