Best Known (75−22, 75, s)-Nets in Base 128
(75−22, 75, 190779)-Net over F128 — Constructive and digital
Digital (53, 75, 190779)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (42, 64, 190650)-net over F128, using
- net defined by OOA [i] based on linear OOA(12864, 190650, F128, 22, 22) (dual of [(190650, 22), 4194236, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(12864, 2097150, F128, 22) (dual of [2097150, 2097086, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(12864, 2097150, F128, 22) (dual of [2097150, 2097086, 23]-code), using
- net defined by OOA [i] based on linear OOA(12864, 190650, F128, 22, 22) (dual of [(190650, 22), 4194236, 23]-NRT-code), using
- digital (0, 11, 129)-net over F128, using
(75−22, 75, 762600)-Net in Base 128 — Constructive
(53, 75, 762600)-net in base 128, using
- 1281 times duplication [i] based on (52, 74, 762600)-net in base 128, using
- net defined by OOA [i] based on OOA(12874, 762600, S128, 22, 22), using
- OA 11-folding and stacking [i] based on OA(12874, 8388600, S128, 22), using
- discarding factors based on OA(12874, large, S128, 22), using
- discarding parts of the base [i] based on linear OA(25664, large, F256, 22) (dual of [large, large−64, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding parts of the base [i] based on linear OA(25664, large, F256, 22) (dual of [large, large−64, 23]-code), using
- discarding factors based on OA(12874, large, S128, 22), using
- OA 11-folding and stacking [i] based on OA(12874, 8388600, S128, 22), using
- net defined by OOA [i] based on OOA(12874, 762600, S128, 22, 22), using
(75−22, 75, 2293194)-Net over F128 — Digital
Digital (53, 75, 2293194)-net over F128, using
(75−22, 75, large)-Net in Base 128 — Upper bound on s
There is no (53, 75, large)-net in base 128, because
- 20 times m-reduction [i] would yield (53, 55, large)-net in base 128, but