Best Known (133, 133+22, s)-Nets in Base 3
(133, 133+22, 16104)-Net over F3 — Constructive and digital
Digital (133, 155, 16104)-net over F3, using
- net defined by OOA [i] based on linear OOA(3155, 16104, F3, 22, 22) (dual of [(16104, 22), 354133, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3155, 177144, F3, 22) (dual of [177144, 176989, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3155, 177144, F3, 22) (dual of [177144, 176989, 23]-code), using
(133, 133+22, 44286)-Net over F3 — Digital
Digital (133, 155, 44286)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3155, 44286, F3, 4, 22) (dual of [(44286, 4), 176989, 23]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3155, 177144, F3, 22) (dual of [177144, 176989, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using
- OOA 4-folding [i] based on linear OA(3155, 177144, F3, 22) (dual of [177144, 176989, 23]-code), using
(133, 133+22, large)-Net in Base 3 — Upper bound on s
There is no (133, 155, large)-net in base 3, because
- 20 times m-reduction [i] would yield (133, 135, large)-net in base 3, but