MinT - Best Known (187, 187+23, s)-Nets in Base 2

Best Known (187, 187+23, s)-Nets in Base 2

Digital (187, 210, 47662)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²¹⁰, 47662, F₂, 23, 23) (dual of [(47662, 23), 1096016, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2²¹⁰, 524283, F₂, 23) (dual of [524283, 524073, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²¹⁰, 524288, F₂, 23) (dual of [524288, 524078, 24]-code), using
    - an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

Digital (187, 210, 74898)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²¹⁰, 74898, F₂, 7, 23) (dual of [(74898, 7), 524076, 24]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2²¹⁰, 524286, F₂, 23) (dual of [524286, 524076, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²¹⁰, 524288, F₂, 23) (dual of [524288, 524078, 24]-code), using
    - an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

There is no (187, 210, 2573839)-net in base 2, because

1 times m-reduction [i] would yield (187, 209, 2573839)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 822 752344 359939 309039 349179 970064 674405 416583 067464 764100 020450 > 2²⁰⁹ [i]