Best Known (70, 70+23, s)-Nets in Base 27
(70, 70+23, 48314)-Net over F27 — Constructive and digital
Digital (70, 93, 48314)-net over F27, using
- 272 times duplication [i] based on digital (68, 91, 48314)-net over F27, using
- net defined by OOA [i] based on linear OOA(2791, 48314, F27, 23, 23) (dual of [(48314, 23), 1111131, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2791, 531455, F27, 23) (dual of [531455, 531364, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(2789, 531441, F27, 23) (dual of [531441, 531352, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2777, 531441, F27, 20) (dual of [531441, 531364, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(272, 14, F27, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- OOA 11-folding and stacking with additional row [i] based on linear OA(2791, 531455, F27, 23) (dual of [531455, 531364, 24]-code), using
- net defined by OOA [i] based on linear OOA(2791, 48314, F27, 23, 23) (dual of [(48314, 23), 1111131, 24]-NRT-code), using
(70, 70+23, 531465)-Net over F27 — Digital
Digital (70, 93, 531465)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2793, 531465, F27, 23) (dual of [531465, 531372, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(2789, 531441, F27, 23) (dual of [531441, 531352, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2769, 531441, F27, 18) (dual of [531441, 531372, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(274, 24, F27, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,27)), using
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- Reed–Solomon code RS(23,27) [i]
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
(70, 70+23, large)-Net in Base 27 — Upper bound on s
There is no (70, 93, large)-net in base 27, because
- 21 times m-reduction [i] would yield (70, 72, large)-net in base 27, but