Best Known (111−16, 111, s)-Nets in Base 3
(111−16, 111, 22143)-Net over F3 — Constructive and digital
Digital (95, 111, 22143)-net over F3, using
- net defined by OOA [i] based on linear OOA(3111, 22143, F3, 16, 16) (dual of [(22143, 16), 354177, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3111, 177144, F3, 16) (dual of [177144, 177033, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3111, 177144, F3, 16) (dual of [177144, 177033, 17]-code), using
(111−16, 111, 52039)-Net over F3 — Digital
Digital (95, 111, 52039)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3111, 52039, F3, 3, 16) (dual of [(52039, 3), 156006, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3111, 59049, F3, 3, 16) (dual of [(59049, 3), 177036, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OOA 3-folding [i] based on linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(3111, 59049, F3, 3, 16) (dual of [(59049, 3), 177036, 17]-NRT-code), using
(111−16, 111, 7847242)-Net in Base 3 — Upper bound on s
There is no (95, 111, 7847243)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 91297 644532 192350 821145 320617 037631 205448 228606 504049 > 3111 [i]