Best Known (126−32, 126, s)-Nets in Base 3
(126−32, 126, 282)-Net over F3 — Constructive and digital
Digital (94, 126, 282)-net over F3, using
- trace code for nets [i] based on digital (10, 42, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
(126−32, 126, 560)-Net over F3 — Digital
Digital (94, 126, 560)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3126, 560, F3, 32) (dual of [560, 434, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3126, 738, F3, 32) (dual of [738, 612, 33]-code), using
- construction XX applied to Ce(31) ⊂ Ce(30) ⊂ Ce(28) [i] based on
- linear OA(3124, 729, F3, 32) (dual of [729, 605, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3118, 729, F3, 31) (dual of [729, 611, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3112, 729, F3, 29) (dual of [729, 617, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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
- 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(31) ⊂ Ce(30) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(3126, 738, F3, 32) (dual of [738, 612, 33]-code), using
(126−32, 126, 19430)-Net in Base 3 — Upper bound on s
There is no (94, 126, 19431)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 310151 914765 301693 765556 220679 031732 881427 960887 904129 400033 > 3126 [i]