Best Known (104, 122, s)-Nets in Base 5
(104, 122, 43409)-Net over F5 — Constructive and digital
Digital (104, 122, 43409)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 6)-net over F5, using
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 0 and N(F) ≥ 6, using
- the rational function field F5(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- digital (95, 113, 43403)-net over F5, using
- net defined by OOA [i] based on linear OOA(5113, 43403, F5, 18, 18) (dual of [(43403, 18), 781141, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(5113, 390627, F5, 18) (dual of [390627, 390514, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(5113, 390633, F5, 18) (dual of [390633, 390520, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(5113, 390625, F5, 18) (dual of [390625, 390512, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(5105, 390625, F5, 17) (dual of [390625, 390520, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(50, 8, F5, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(5113, 390633, F5, 18) (dual of [390633, 390520, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(5113, 390627, F5, 18) (dual of [390627, 390514, 19]-code), using
- net defined by OOA [i] based on linear OOA(5113, 43403, F5, 18, 18) (dual of [(43403, 18), 781141, 19]-NRT-code), using
- digital (0, 9, 6)-net over F5, using
(104, 122, 328416)-Net over F5 — Digital
Digital (104, 122, 328416)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5122, 328416, F5, 18) (dual of [328416, 328294, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(5122, 390635, F5, 18) (dual of [390635, 390513, 19]-code), using
- (u, u+v)-construction [i] based on
- linear OA(59, 10, F5, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,5)), using
- dual of repetition code with length 10 [i]
- linear OA(5113, 390625, F5, 18) (dual of [390625, 390512, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(59, 10, F5, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,5)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(5122, 390635, F5, 18) (dual of [390635, 390513, 19]-code), using
(104, 122, large)-Net in Base 5 — Upper bound on s
There is no (104, 122, large)-net in base 5, because
- 16 times m-reduction [i] would yield (104, 106, large)-net in base 5, but