Best Known (72, 72+23, s)-Nets in Base 8
(72, 72+23, 746)-Net over F8 — Constructive and digital
Digital (72, 95, 746)-net over F8, using
- 81 times duplication [i] based on digital (71, 94, 746)-net over F8, using
- net defined by OOA [i] based on linear OOA(894, 746, F8, 23, 23) (dual of [(746, 23), 17064, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(894, 8207, F8, 23) (dual of [8207, 8113, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(894, 8208, F8, 23) (dual of [8208, 8114, 24]-code), using
- trace code [i] based on linear OA(6447, 4104, F64, 23) (dual of [4104, 4057, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(6445, 4096, F64, 23) (dual of [4096, 4051, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(6439, 4096, F64, 20) (dual of [4096, 4057, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(642, 8, F64, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(6447, 4104, F64, 23) (dual of [4104, 4057, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(894, 8208, F8, 23) (dual of [8208, 8114, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(894, 8207, F8, 23) (dual of [8207, 8113, 24]-code), using
- net defined by OOA [i] based on linear OOA(894, 746, F8, 23, 23) (dual of [(746, 23), 17064, 24]-NRT-code), using
(72, 72+23, 1030)-Net in Base 8 — Constructive
(72, 95, 1030)-net in base 8, using
- 81 times duplication [i] based on (71, 94, 1030)-net in base 8, using
- (u, u+v)-construction [i] based on
- (19, 30, 514)-net in base 8, using
- trace code for nets [i] based on (4, 15, 257)-net in base 64, using
- 1 times m-reduction [i] based on (4, 16, 257)-net in base 64, using
- base change [i] based on digital (0, 12, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 12, 257)-net over F256, using
- 1 times m-reduction [i] based on (4, 16, 257)-net in base 64, using
- trace code for nets [i] based on (4, 15, 257)-net in base 64, using
- (41, 64, 516)-net in base 8, using
- base change [i] based on digital (25, 48, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 24, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 24, 258)-net over F256, using
- base change [i] based on digital (25, 48, 516)-net over F16, using
- (19, 30, 514)-net in base 8, using
- (u, u+v)-construction [i] based on
(72, 72+23, 10278)-Net over F8 — Digital
Digital (72, 95, 10278)-net over F8, using
(72, 72+23, large)-Net in Base 8 — Upper bound on s
There is no (72, 95, large)-net in base 8, because
- 21 times m-reduction [i] would yield (72, 74, large)-net in base 8, but