Best Known (75, 75+21, s)-Nets in Base 27
(75, 75+21, 53212)-Net over F27 — Constructive and digital
Digital (75, 96, 53212)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (60, 81, 53144)-net over F27, using
- net defined by OOA [i] based on linear OOA(2781, 53144, F27, 21, 21) (dual of [(53144, 21), 1115943, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on 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]
- OOA 10-folding and stacking with additional row [i] based on linear OA(2781, 531441, F27, 21) (dual of [531441, 531360, 22]-code), using
- net defined by OOA [i] based on linear OOA(2781, 53144, F27, 21, 21) (dual of [(53144, 21), 1115943, 22]-NRT-code), using
- digital (5, 15, 68)-net over F27, using
(75, 75+21, 53244)-Net in Base 27 — Constructive
(75, 96, 53244)-net in base 27, using
- base change [i] based on digital (51, 72, 53244)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 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
- digital (40, 61, 53144)-net over F81, using
- net defined by OOA [i] based on linear OOA(8161, 53144, F81, 21, 21) (dual of [(53144, 21), 1115963, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- OOA 10-folding and stacking with additional row [i] based on linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using
- net defined by OOA [i] based on linear OOA(8161, 53144, F81, 21, 21) (dual of [(53144, 21), 1115963, 22]-NRT-code), using
- digital (1, 11, 100)-net over F81, using
- (u, u+v)-construction [i] based on
(75, 75+21, 2370723)-Net over F27 — Digital
Digital (75, 96, 2370723)-net over F27, using
(75, 75+21, large)-Net in Base 27 — Upper bound on s
There is no (75, 96, large)-net in base 27, because
- 19 times m-reduction [i] would yield (75, 77, large)-net in base 27, but