Best Known (80, 102, s)-Nets in Base 27
(80, 102, 48389)-Net over F27 — Constructive and digital
Digital (80, 102, 48389)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 17, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, 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
- digital (6, 17, 76)-net over F27, using
(80, 102, 48413)-Net in Base 27 — Constructive
(80, 102, 48413)-net in base 27, using
- 271 times duplication [i] based on (79, 101, 48413)-net in base 27, using
- (u, u+v)-construction [i] based on
- (5, 16, 100)-net in base 27, using
- base change [i] based on digital (1, 12, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- base change [i] based on digital (1, 12, 100)-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
- (5, 16, 100)-net in base 27, using
- (u, u+v)-construction [i] based on
(80, 102, 2991293)-Net over F27 — Digital
Digital (80, 102, 2991293)-net over F27, using
(80, 102, large)-Net in Base 27 — Upper bound on s
There is no (80, 102, large)-net in base 27, because
- 20 times m-reduction [i] would yield (80, 82, large)-net in base 27, but