Best Known (30, 35, s)-Nets in Base 3
(30, 35, 88579)-Net over F3 — Constructive and digital
Digital (30, 35, 88579)-net over F3, using
- net defined by OOA [i] based on linear OOA(335, 88579, F3, 5, 5) (dual of [(88579, 5), 442860, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(335, 177159, F3, 5) (dual of [177159, 177124, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(335, 177160, F3, 5) (dual of [177160, 177125, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(334, 177147, F3, 5) (dual of [177147, 177113, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(323, 177147, F3, 4) (dual of [177147, 177124, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(312, 13, F3, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,3)), using
- dual of repetition code with length 13 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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 X4 applied to Ce(4) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(335, 177160, F3, 5) (dual of [177160, 177125, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(335, 177159, F3, 5) (dual of [177159, 177124, 6]-code), using
(30, 35, 177160)-Net over F3 — Digital
Digital (30, 35, 177160)-net over F3, using
- net defined by OOA [i] based on linear OOA(335, 177160, F3, 5, 5) (dual of [(177160, 5), 885765, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(335, 177160, F3, 4, 5) (dual of [(177160, 4), 708605, 6]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(335, 177160, F3, 5) (dual of [177160, 177125, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(334, 177147, F3, 5) (dual of [177147, 177113, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(323, 177147, F3, 4) (dual of [177147, 177124, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(312, 13, F3, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,3)), using
- dual of repetition code with length 13 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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 X4 applied to Ce(4) ⊂ Ce(3) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(335, 177160, F3, 5) (dual of [177160, 177125, 6]-code), using
- appending kth column [i] based on linear OOA(335, 177160, F3, 4, 5) (dual of [(177160, 4), 708605, 6]-NRT-code), using
(30, 35, large)-Net in Base 3 — Upper bound on s
There is no (30, 35, large)-net in base 3, because
- 3 times m-reduction [i] would yield (30, 32, large)-net in base 3, but