Best Known (103−23, 103, s)-Nets in Base 32
(103−23, 103, 95389)-Net over F32 — Constructive and digital
Digital (80, 103, 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 (66, 89, 95325)-net over F32, using
- net defined by OOA [i] based on linear OOA(3289, 95325, F32, 23, 23) (dual of [(95325, 23), 2192386, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 11-folding and stacking with additional row [i] based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
- net defined by OOA [i] based on linear OOA(3289, 95325, F32, 23, 23) (dual of [(95325, 23), 2192386, 24]-NRT-code), using
- digital (3, 14, 64)-net over F32, using
(103−23, 103, 190652)-Net in Base 32 — Constructive
(80, 103, 190652)-net in base 32, using
- 321 times duplication [i] based on (79, 102, 190652)-net in base 32, using
- base change [i] based on (62, 85, 190652)-net in base 64, using
- 641 times duplication [i] based on (61, 84, 190652)-net in base 64, using
- base change [i] based on digital (49, 72, 190652)-net over F128, using
- net defined by OOA [i] based on linear OOA(12872, 190652, F128, 23, 23) (dual of [(190652, 23), 4384924, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12872, 2097173, F128, 23) (dual of [2097173, 2097101, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(12872, 2097176, F128, 23) (dual of [2097176, 2097104, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,8]) [i] based on
- linear OA(12867, 2097153, F128, 23) (dual of [2097153, 2097086, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [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 C([0,11]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12872, 2097176, F128, 23) (dual of [2097176, 2097104, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12872, 2097173, F128, 23) (dual of [2097173, 2097101, 24]-code), using
- net defined by OOA [i] based on linear OOA(12872, 190652, F128, 23, 23) (dual of [(190652, 23), 4384924, 24]-NRT-code), using
- base change [i] based on digital (49, 72, 190652)-net over F128, using
- 641 times duplication [i] based on (61, 84, 190652)-net in base 64, using
- base change [i] based on (62, 85, 190652)-net in base 64, using
(103−23, 103, 3253354)-Net over F32 — Digital
Digital (80, 103, 3253354)-net over F32, using
(103−23, 103, large)-Net in Base 32 — Upper bound on s
There is no (80, 103, large)-net in base 32, because
- 21 times m-reduction [i] would yield (80, 82, large)-net in base 32, but