Best Known (106, 106+22, s)-Nets in Base 3
(106, 106+22, 1790)-Net over F3 — Constructive and digital
Digital (106, 128, 1790)-net over F3, using
- net defined by OOA [i] based on linear OOA(3128, 1790, F3, 22, 22) (dual of [(1790, 22), 39252, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3128, 19690, F3, 22) (dual of [19690, 19562, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3128, 19693, F3, 22) (dual of [19693, 19565, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3128, 19693, F3, 22) (dual of [19693, 19565, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3128, 19690, F3, 22) (dual of [19690, 19562, 23]-code), using
(106, 106+22, 6564)-Net over F3 — Digital
Digital (106, 128, 6564)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3128, 6564, F3, 3, 22) (dual of [(6564, 3), 19564, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3128, 19692, F3, 22) (dual of [19692, 19564, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3128, 19693, F3, 22) (dual of [19693, 19565, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3128, 19693, F3, 22) (dual of [19693, 19565, 23]-code), using
- OOA 3-folding [i] based on linear OA(3128, 19692, F3, 22) (dual of [19692, 19564, 23]-code), using
(106, 106+22, 874853)-Net in Base 3 — Upper bound on s
There is no (106, 128, 874854)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 11 790248 815094 933660 789014 352762 425059 786595 745409 266187 899281 > 3128 [i]