Best Known (121−26, 121, s)-Nets in Base 3
(121−26, 121, 600)-Net over F3 — Constructive and digital
Digital (95, 121, 600)-net over F3, using
- 31 times duplication [i] based on digital (94, 120, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 30, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 30, 150)-net over F81, using
(121−26, 121, 1169)-Net over F3 — Digital
Digital (95, 121, 1169)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3121, 1169, F3, 26) (dual of [1169, 1048, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3121, 2195, F3, 26) (dual of [2195, 2074, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3120, 2194, F3, 26) (dual of [2194, 2074, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(3120, 2187, F3, 26) (dual of [2187, 2067, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3113, 2187, F3, 25) (dual of [2187, 2074, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(30, 7, F3, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3120, 2194, F3, 26) (dual of [2194, 2074, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3121, 2195, F3, 26) (dual of [2195, 2074, 27]-code), using
(121−26, 121, 78199)-Net in Base 3 — Upper bound on s
There is no (95, 121, 78200)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 5391 377608 706109 644792 013392 088107 274302 296080 683778 617841 > 3121 [i]