Best Known (30−9, 30, s)-Nets in Base 64
(30−9, 30, 65616)-Net over F64 — Constructive and digital
Digital (21, 30, 65616)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (16, 25, 65536)-net over F64, using
- net defined by OOA [i] based on linear OOA(6425, 65536, F64, 9, 9) (dual of [(65536, 9), 589799, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(6425, 262145, F64, 9) (dual of [262145, 262120, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(6425, 262145, F64, 9) (dual of [262145, 262120, 10]-code), using
- net defined by OOA [i] based on linear OOA(6425, 65536, F64, 9, 9) (dual of [(65536, 9), 589799, 10]-NRT-code), using
- digital (1, 5, 80)-net over F64, using
(30−9, 30, 354429)-Net over F64 — Digital
Digital (21, 30, 354429)-net over F64, using
(30−9, 30, 524288)-Net in Base 64 — Constructive
(21, 30, 524288)-net in base 64, using
- net defined by OOA [i] based on OOA(6430, 524288, S64, 9, 9), using
- OOA 4-folding and stacking with additional row [i] based on OA(6430, 2097153, S64, 9), using
- discarding factors based on OA(6430, 2097155, S64, 9), using
- discarding parts of the base [i] based on linear OA(12825, 2097155, F128, 9) (dual of [2097155, 2097130, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- discarding parts of the base [i] based on linear OA(12825, 2097155, F128, 9) (dual of [2097155, 2097130, 10]-code), using
- discarding factors based on OA(6430, 2097155, S64, 9), using
- OOA 4-folding and stacking with additional row [i] based on OA(6430, 2097153, S64, 9), using
(30−9, 30, large)-Net in Base 64 — Upper bound on s
There is no (21, 30, large)-net in base 64, because
- 7 times m-reduction [i] would yield (21, 23, large)-net in base 64, but