Best Known (83, 105, s)-Nets in Base 27
(83, 105, 48409)-Net over F27 — Constructive and digital
Digital (83, 105, 48409)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 20, 96)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 351)-net over F27, using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- digital (2, 13, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- digital (2, 7, 351)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (63, 85, 48313)-net over F27, using
- net defined by OOA [i] based on linear OOA(2785, 48313, F27, 22, 22) (dual of [(48313, 22), 1062801, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2785, 531443, F27, 22) (dual of [531443, 531358, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2785, 531445, F27, 22) (dual of [531445, 531360, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(2785, 531441, F27, 22) (dual of [531441, 531356, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2781, 531441, F27, 21) (dual of [531441, 531360, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2785, 531445, F27, 22) (dual of [531445, 531360, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2785, 531443, F27, 22) (dual of [531443, 531358, 23]-code), using
- net defined by OOA [i] based on linear OOA(2785, 48313, F27, 22, 22) (dual of [(48313, 22), 1062801, 23]-NRT-code), using
- digital (9, 20, 96)-net over F27, using
(83, 105, 48463)-Net in Base 27 — Constructive
(83, 105, 48463)-net in base 27, using
- (u, u+v)-construction [i] based on
- (9, 20, 150)-net in base 27, using
- base change [i] based on digital (4, 15, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- base change [i] based on digital (4, 15, 150)-net over F81, using
- digital (63, 85, 48313)-net over F27, using
- net defined by OOA [i] based on linear OOA(2785, 48313, F27, 22, 22) (dual of [(48313, 22), 1062801, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2785, 531443, F27, 22) (dual of [531443, 531358, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2785, 531445, F27, 22) (dual of [531445, 531360, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(2785, 531441, F27, 22) (dual of [531441, 531356, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2781, 531441, F27, 21) (dual of [531441, 531360, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2785, 531445, F27, 22) (dual of [531445, 531360, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2785, 531443, F27, 22) (dual of [531443, 531358, 23]-code), using
- net defined by OOA [i] based on linear OOA(2785, 48313, F27, 22, 22) (dual of [(48313, 22), 1062801, 23]-NRT-code), using
- (9, 20, 150)-net in base 27, using
(83, 105, 4790038)-Net over F27 — Digital
Digital (83, 105, 4790038)-net over F27, using
(83, 105, large)-Net in Base 27 — Upper bound on s
There is no (83, 105, large)-net in base 27, because
- 20 times m-reduction [i] would yield (83, 85, large)-net in base 27, but