Best Known (91−11, 91, s)-Nets in Base 7
(91−11, 91, 2305970)-Net over F7 — Constructive and digital
Digital (80, 91, 2305970)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (4, 9, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(4,49) in PG(8,7)) for nets [i] based on digital (0, 5, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- base reduction for projective spaces (embedding PG(4,49) in PG(8,7)) for nets [i] based on digital (0, 5, 50)-net over F49, using
- digital (71, 82, 2305920)-net over F7, using
- trace code for nets [i] based on digital (30, 41, 1152960)-net over F49, using
- net defined by OOA [i] based on linear OOA(4941, 1152960, F49, 11, 11) (dual of [(1152960, 11), 12682519, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using
- net defined by OOA [i] based on linear OOA(4941, 1152960, F49, 11, 11) (dual of [(1152960, 11), 12682519, 12]-NRT-code), using
- trace code for nets [i] based on digital (30, 41, 1152960)-net over F49, using
- digital (4, 9, 50)-net over F7, using
(91−11, 91, large)-Net over F7 — Digital
Digital (80, 91, large)-net over F7, using
- 71 times duplication [i] based on digital (79, 90, large)-net over F7, using
- t-expansion [i] based on digital (78, 90, large)-net over F7, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(790, large, F7, 12) (dual of [large, large−90, 13]-code), using
- trace code [i] based on linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- trace code [i] based on linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(790, large, F7, 12) (dual of [large, large−90, 13]-code), using
- t-expansion [i] based on digital (78, 90, large)-net over F7, using
(91−11, 91, large)-Net in Base 7 — Upper bound on s
There is no (80, 91, large)-net in base 7, because
- 9 times m-reduction [i] would yield (80, 82, large)-net in base 7, but