Best Known (99−22, 99, s)-Nets in Base 32
(99−22, 99, 95389)-Net over F32 — Constructive and digital
Digital (77, 99, 95389)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (63, 85, 95325)-net over F32, using
- net defined by OOA [i] based on linear OOA(3285, 95325, F32, 22, 22) (dual of [(95325, 22), 2097065, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3285, 1048575, F32, 22) (dual of [1048575, 1048490, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3285, 1048575, F32, 22) (dual of [1048575, 1048490, 23]-code), using
- net defined by OOA [i] based on linear OOA(3285, 95325, F32, 22, 22) (dual of [(95325, 22), 2097065, 23]-NRT-code), using
- digital (3, 14, 64)-net over F32, using
(99−22, 99, 190652)-Net in Base 32 — Constructive
(77, 99, 190652)-net in base 32, using
- 321 times duplication [i] based on (76, 98, 190652)-net in base 32, using
- base change [i] based on digital (48, 70, 190652)-net over F128, using
- 1281 times duplication [i] based on digital (47, 69, 190652)-net over F128, using
- net defined by OOA [i] based on linear OOA(12869, 190652, F128, 22, 22) (dual of [(190652, 22), 4194275, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(12869, 2097172, F128, 22) (dual of [2097172, 2097103, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12869, 2097175, F128, 22) (dual of [2097175, 2097106, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] 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]
- linear OA(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(1285, 23, F128, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(12869, 2097175, F128, 22) (dual of [2097175, 2097106, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(12869, 2097172, F128, 22) (dual of [2097172, 2097103, 23]-code), using
- net defined by OOA [i] based on linear OOA(12869, 190652, F128, 22, 22) (dual of [(190652, 22), 4194275, 23]-NRT-code), using
- 1281 times duplication [i] based on digital (47, 69, 190652)-net over F128, using
- base change [i] based on digital (48, 70, 190652)-net over F128, using
(99−22, 99, 3490111)-Net over F32 — Digital
Digital (77, 99, 3490111)-net over F32, using
(99−22, 99, large)-Net in Base 32 — Upper bound on s
There is no (77, 99, large)-net in base 32, because
- 20 times m-reduction [i] would yield (77, 79, large)-net in base 32, but