Best Known (53, 73, s)-Nets in Base 32
(53, 73, 3353)-Net over F32 — Constructive and digital
Digital (53, 73, 3353)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (38, 58, 3277)-net over F32, using
- net defined by OOA [i] based on linear OOA(3258, 3277, F32, 20, 20) (dual of [(3277, 20), 65482, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3258, 32770, F32, 20) (dual of [32770, 32712, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3258, 32771, F32, 20) (dual of [32771, 32713, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3255, 32768, F32, 19) (dual of [32768, 32713, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3258, 32771, F32, 20) (dual of [32771, 32713, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3258, 32770, F32, 20) (dual of [32770, 32712, 21]-code), using
- net defined by OOA [i] based on linear OOA(3258, 3277, F32, 20, 20) (dual of [(3277, 20), 65482, 21]-NRT-code), using
- digital (5, 15, 76)-net over F32, using
(53, 73, 26215)-Net in Base 32 — Constructive
(53, 73, 26215)-net in base 32, using
- 321 times duplication [i] based on (52, 72, 26215)-net in base 32, using
- base change [i] based on digital (40, 60, 26215)-net over F64, using
- 641 times duplication [i] based on digital (39, 59, 26215)-net over F64, using
- net defined by OOA [i] based on linear OOA(6459, 26215, F64, 20, 20) (dual of [(26215, 20), 524241, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(6459, 262150, F64, 20) (dual of [262150, 262091, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(6459, 262151, F64, 20) (dual of [262151, 262092, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(6459, 262151, F64, 20) (dual of [262151, 262092, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(6459, 262150, F64, 20) (dual of [262150, 262091, 21]-code), using
- net defined by OOA [i] based on linear OOA(6459, 26215, F64, 20, 20) (dual of [(26215, 20), 524241, 21]-NRT-code), using
- 641 times duplication [i] based on digital (39, 59, 26215)-net over F64, using
- base change [i] based on digital (40, 60, 26215)-net over F64, using
(53, 73, 155176)-Net over F32 — Digital
Digital (53, 73, 155176)-net over F32, using
(53, 73, large)-Net in Base 32 — Upper bound on s
There is no (53, 73, large)-net in base 32, because
- 18 times m-reduction [i] would yield (53, 55, large)-net in base 32, but