Best Known (96, 96+26, s)-Nets in Base 3
(96, 96+26, 600)-Net over F3 — Constructive and digital
Digital (96, 122, 600)-net over F3, using
- 32 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
(96, 96+26, 1225)-Net over F3 — Digital
Digital (96, 122, 1225)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3122, 1225, F3, 26) (dual of [1225, 1103, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3122, 2197, F3, 26) (dual of [2197, 2075, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(24) ⊂ Ce(22) [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(3106, 2187, F3, 23) (dual of [2187, 2081, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 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
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(25) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3122, 2197, F3, 26) (dual of [2197, 2075, 27]-code), using
(96, 96+26, 85096)-Net in Base 3 — Upper bound on s
There is no (96, 122, 85097)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 16174 247519 467586 305422 157039 445875 388103 582527 111672 073891 > 3122 [i]