Best Known (78, 78+24, s)-Nets in Base 32
(78, 78+24, 87385)-Net over F32 — Constructive and digital
Digital (78, 102, 87385)-net over F32, using
- net defined by OOA [i] based on linear OOA(32102, 87385, F32, 24, 24) (dual of [(87385, 24), 2097138, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(32102, 1048620, F32, 24) (dual of [1048620, 1048518, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(14) [i] based on
- linear OA(3293, 1048576, F32, 24) (dual of [1048576, 1048483, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3257, 1048576, F32, 15) (dual of [1048576, 1048519, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(329, 44, F32, 8) (dual of [44, 35, 9]-code), using
- extended algebraic-geometric code AGe(F,35P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- construction X applied to Ce(23) ⊂ Ce(14) [i] based on
- OA 12-folding and stacking [i] based on linear OA(32102, 1048620, F32, 24) (dual of [1048620, 1048518, 25]-code), using
(78, 78+24, 174763)-Net in Base 32 — Constructive
(78, 102, 174763)-net in base 32, using
- base change [i] based on (61, 85, 174763)-net in base 64, using
- 641 times duplication [i] based on (60, 84, 174763)-net in base 64, using
- base change [i] based on digital (48, 72, 174763)-net over F128, using
- 1281 times duplication [i] based on digital (47, 71, 174763)-net over F128, using
- net defined by OOA [i] based on linear OOA(12871, 174763, F128, 24, 24) (dual of [(174763, 24), 4194241, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(12871, 2097156, F128, 24) (dual of [2097156, 2097085, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(12871, 2097159, F128, 24) (dual of [2097159, 2097088, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(12870, 2097152, F128, 24) (dual of [2097152, 2097082, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- 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(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(12871, 2097159, F128, 24) (dual of [2097159, 2097088, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(12871, 2097156, F128, 24) (dual of [2097156, 2097085, 25]-code), using
- net defined by OOA [i] based on linear OOA(12871, 174763, F128, 24, 24) (dual of [(174763, 24), 4194241, 25]-NRT-code), using
- 1281 times duplication [i] based on digital (47, 71, 174763)-net over F128, using
- base change [i] based on digital (48, 72, 174763)-net over F128, using
- 641 times duplication [i] based on (60, 84, 174763)-net in base 64, using
(78, 78+24, 1439166)-Net over F32 — Digital
Digital (78, 102, 1439166)-net over F32, using
(78, 78+24, large)-Net in Base 32 — Upper bound on s
There is no (78, 102, large)-net in base 32, because
- 22 times m-reduction [i] would yield (78, 80, large)-net in base 32, but