Best Known (236−33, 236, s)-Nets in Base 3
(236−33, 236, 3694)-Net over F3 — Constructive and digital
Digital (203, 236, 3694)-net over F3, using
- net defined by OOA [i] based on linear OOA(3236, 3694, F3, 33, 33) (dual of [(3694, 33), 121666, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(3236, 59105, F3, 33) (dual of [59105, 58869, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 59114, F3, 33) (dual of [59114, 58878, 34]-code), using
- 1 times truncation [i] based on linear OA(3237, 59115, F3, 34) (dual of [59115, 58878, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(316, 66, F3, 7) (dual of [66, 50, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- 1 times truncation [i] based on linear OA(3237, 59115, F3, 34) (dual of [59115, 58878, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 59114, F3, 33) (dual of [59114, 58878, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(3236, 59105, F3, 33) (dual of [59105, 58869, 34]-code), using
(236−33, 236, 29557)-Net over F3 — Digital
Digital (203, 236, 29557)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3236, 29557, F3, 2, 33) (dual of [(29557, 2), 58878, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3236, 59114, F3, 33) (dual of [59114, 58878, 34]-code), using
- 1 times truncation [i] based on linear OA(3237, 59115, F3, 34) (dual of [59115, 58878, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(316, 66, F3, 7) (dual of [66, 50, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- 1 times truncation [i] based on linear OA(3237, 59115, F3, 34) (dual of [59115, 58878, 35]-code), using
- OOA 2-folding [i] based on linear OA(3236, 59114, F3, 33) (dual of [59114, 58878, 34]-code), using
(236−33, 236, large)-Net in Base 3 — Upper bound on s
There is no (203, 236, large)-net in base 3, because
- 31 times m-reduction [i] would yield (203, 205, large)-net in base 3, but