Best Known (84, 107, s)-Nets in Base 27
(84, 107, 48395)-Net over F27 — Constructive and digital
Digital (84, 107, 48395)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 18, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (66, 89, 48313)-net over F27, using
- net defined by OOA [i] based on linear OOA(2789, 48313, F27, 23, 23) (dual of [(48313, 23), 1111110, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2789, 531444, F27, 23) (dual of [531444, 531355, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2789, 531445, F27, 23) (dual of [531445, 531356, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(2789, 531441, F27, 23) (dual of [531441, 531352, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(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(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(2789, 531445, F27, 23) (dual of [531445, 531356, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2789, 531444, F27, 23) (dual of [531444, 531355, 24]-code), using
- net defined by OOA [i] based on linear OOA(2789, 48313, F27, 23, 23) (dual of [(48313, 23), 1111110, 24]-NRT-code), using
- digital (7, 18, 82)-net over F27, using
(84, 107, 48429)-Net in Base 27 — Constructive
(84, 107, 48429)-net in base 27, using
- (u, u+v)-construction [i] based on
- (7, 18, 116)-net in base 27, using
- 2 times m-reduction [i] based on (7, 20, 116)-net in base 27, using
- base change [i] based on digital (2, 15, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 15, 116)-net over F81, using
- 2 times m-reduction [i] based on (7, 20, 116)-net in base 27, using
- digital (66, 89, 48313)-net over F27, using
- net defined by OOA [i] based on linear OOA(2789, 48313, F27, 23, 23) (dual of [(48313, 23), 1111110, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2789, 531444, F27, 23) (dual of [531444, 531355, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2789, 531445, F27, 23) (dual of [531445, 531356, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(2789, 531441, F27, 23) (dual of [531441, 531352, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(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(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(2789, 531445, F27, 23) (dual of [531445, 531356, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2789, 531444, F27, 23) (dual of [531444, 531355, 24]-code), using
- net defined by OOA [i] based on linear OOA(2789, 48313, F27, 23, 23) (dual of [(48313, 23), 1111110, 24]-NRT-code), using
- (7, 18, 116)-net in base 27, using
(84, 107, 3187969)-Net over F27 — Digital
Digital (84, 107, 3187969)-net over F27, using
(84, 107, large)-Net in Base 27 — Upper bound on s
There is no (84, 107, large)-net in base 27, because
- 21 times m-reduction [i] would yield (84, 86, large)-net in base 27, but