Best Known (90−25, 90, s)-Nets in Base 64
(90−25, 90, 21973)-Net over F64 — Constructive and digital
Digital (65, 90, 21973)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (5, 17, 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 (48, 73, 21845)-net over F64, using
- net defined by OOA [i] based on linear OOA(6473, 21845, F64, 25, 25) (dual of [(21845, 25), 546052, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(6473, 262141, F64, 25) (dual of [262141, 262068, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(6473, 262141, F64, 25) (dual of [262141, 262068, 26]-code), using
- net defined by OOA [i] based on linear OOA(6473, 21845, F64, 25, 25) (dual of [(21845, 25), 546052, 26]-NRT-code), using
- digital (5, 17, 128)-net over F64, using
(90−25, 90, 174764)-Net in Base 64 — Constructive
(65, 90, 174764)-net in base 64, using
- net defined by OOA [i] based on OOA(6490, 174764, S64, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(6490, 2097169, S64, 25), using
- discarding factors based on OA(6490, 2097171, S64, 25), using
- discarding parts of the base [i] based on linear OA(12877, 2097171, F128, 25) (dual of [2097171, 2097094, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(12873, 2097152, F128, 25) (dual of [2097152, 2097079, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-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(24) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(12877, 2097171, F128, 25) (dual of [2097171, 2097094, 26]-code), using
- discarding factors based on OA(6490, 2097171, S64, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(6490, 2097169, S64, 25), using
(90−25, 90, 923002)-Net over F64 — Digital
Digital (65, 90, 923002)-net over F64, using
(90−25, 90, large)-Net in Base 64 — Upper bound on s
There is no (65, 90, large)-net in base 64, because
- 23 times m-reduction [i] would yield (65, 67, large)-net in base 64, but