Best Known (88−36, 88, s)-Nets in Base 64
(88−36, 88, 641)-Net over F64 — Constructive and digital
Digital (52, 88, 641)-net over F64, using
- 2 times m-reduction [i] based on digital (52, 90, 641)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (5, 24, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- digital (28, 66, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- digital (5, 24, 128)-net over F64, using
- (u, u+v)-construction [i] based on
(88−36, 88, 911)-Net in Base 64 — Constructive
(52, 88, 911)-net in base 64, using
- net defined by OOA [i] based on OOA(6488, 911, S64, 36, 36), using
- OA 18-folding and stacking [i] based on OA(6488, 16398, S64, 36), using
- discarding parts of the base [i] based on linear OA(12875, 16398, F128, 36) (dual of [16398, 16323, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(30) [i] based on
- linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(12861, 16384, F128, 31) (dual of [16384, 16323, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(1284, 14, F128, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(35) ⊂ Ce(30) [i] based on
- discarding parts of the base [i] based on linear OA(12875, 16398, F128, 36) (dual of [16398, 16323, 37]-code), using
- OA 18-folding and stacking [i] based on OA(6488, 16398, S64, 36), using
(88−36, 88, 7694)-Net over F64 — Digital
Digital (52, 88, 7694)-net over F64, using
(88−36, 88, large)-Net in Base 64 — Upper bound on s
There is no (52, 88, large)-net in base 64, because
- 34 times m-reduction [i] would yield (52, 54, large)-net in base 64, but