Best Known (120−16, 120, s)-Nets in Base 3
(120−16, 120, 22150)-Net over F3 — Constructive and digital
Digital (104, 120, 22150)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- 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
- net defined by OOA [i] based on linear OOA(3111, 22143, F3, 16, 16) (dual of [(22143, 16), 354177, 17]-NRT-code), using
- digital (1, 9, 7)-net over F3, using
(120−16, 120, 60685)-Net over F3 — Digital
Digital (104, 120, 60685)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3120, 60685, F3, 2, 16) (dual of [(60685, 2), 121250, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3120, 88594, F3, 2, 16) (dual of [(88594, 2), 177068, 17]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3119, 88594, F3, 2, 16) (dual of [(88594, 2), 177069, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3119, 177188, F3, 16) (dual of [177188, 177069, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [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]
- linear OA(378, 177147, F3, 11) (dual of [177147, 177069, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- OOA 2-folding [i] based on linear OA(3119, 177188, F3, 16) (dual of [177188, 177069, 17]-code), using
- 31 times duplication [i] based on linear OOA(3119, 88594, F3, 2, 16) (dual of [(88594, 2), 177069, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3120, 88594, F3, 2, 16) (dual of [(88594, 2), 177068, 17]-NRT-code), using
(120−16, 120, large)-Net in Base 3 — Upper bound on s
There is no (104, 120, large)-net in base 3, because
- 14 times m-reduction [i] would yield (104, 106, large)-net in base 3, but