Best Known (62, 62+27, s)-Nets in Base 27
(62, 62+27, 1517)-Net over F27 — Constructive and digital
Digital (62, 89, 1517)-net over F27, using
- net defined by OOA [i] based on linear OOA(2789, 1517, F27, 27, 27) (dual of [(1517, 27), 40870, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2789, 19722, F27, 27) (dual of [19722, 19633, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,8]) [i] based on
- linear OA(2779, 19684, F27, 27) (dual of [19684, 19605, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(2749, 19684, F27, 17) (dual of [19684, 19635, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2710, 38, F27, 9) (dual of [38, 28, 10]-code), using
- extended algebraic-geometric code AGe(F,28P) [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- construction X applied to C([0,13]) ⊂ C([0,8]) [i] based on
- OOA 13-folding and stacking with additional row [i] based on linear OA(2789, 19722, F27, 27) (dual of [19722, 19633, 28]-code), using
(62, 62+27, 32223)-Net over F27 — Digital
Digital (62, 89, 32223)-net over F27, using
(62, 62+27, large)-Net in Base 27 — Upper bound on s
There is no (62, 89, large)-net in base 27, because
- 25 times m-reduction [i] would yield (62, 64, large)-net in base 27, but