Best Known (26, 30, s)-Nets in Base 5
(26, 30, 976573)-Net over F5 — Constructive and digital
Digital (26, 30, 976573)-net over F5, using
- net defined by OOA [i] based on linear OOA(530, 976573, F5, 4, 4) (dual of [(976573, 4), 3906262, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(530, 976573, F5, 3, 4) (dual of [(976573, 3), 2929689, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(530, 1953146, F5, 4) (dual of [1953146, 1953116, 5]-code), using
- 1 times code embedding in larger space [i] based on linear OA(529, 1953145, F5, 4) (dual of [1953145, 1953116, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(528, 1953125, F5, 4) (dual of [1953125, 1953097, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(510, 1953125, F5, 2) (dual of [1953125, 1953115, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(519, 20, F5, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,5)), using
- dual of repetition code with length 20 [i]
- linear OA(51, 20, F5, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(529, 1953145, F5, 4) (dual of [1953145, 1953116, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(530, 1953146, F5, 4) (dual of [1953146, 1953116, 5]-code), using
- appending kth column [i] based on linear OOA(530, 976573, F5, 3, 4) (dual of [(976573, 3), 2929689, 5]-NRT-code), using
(26, 30, 4436331)-Net over F5 — Digital
Digital (26, 30, 4436331)-net over F5, using
- net defined by OOA [i] based on linear OOA(530, 4436331, F5, 4, 4) (dual of [(4436331, 4), 17745294, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(530, 4436331, F5, 3, 4) (dual of [(4436331, 3), 13308963, 5]-NRT-code), using
(26, 30, large)-Net in Base 5 — Upper bound on s
There is no (26, 30, large)-net in base 5, because
- 2 times m-reduction [i] would yield (26, 28, large)-net in base 5, but