MinT - Best Known (144−24, 144, s)-Nets in Base 8

Best Known (144−24, 144, s)-Nets in Base 8

(144−24, 144, 43692)-Net over F₈ — Constructive and digital

Digital (120, 144, 43692)-net over F₈, using

net defined by OOA [i] based on linear OOA(8¹⁴⁴, 43692, F₈, 24, 24) (dual of [(43692, 24), 1048464, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8¹⁴⁴, 524304, F₈, 24) (dual of [524304, 524160, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹⁴⁴, 524310, F₈, 24) (dual of [524310, 524166, 25]-code), using
    - trace code [i] based on linear OA(64⁷², 262155, F₆₄, 24) (dual of [262155, 262083, 25]-code), using
      - constructionÂ X applied to C_e(23) âŠ‚ C_e(20) [i] based on
        linear OA(64⁷⁰, 262144, F₆₄, 24) (dual of [262144, 262074, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
        linear OA(64⁶¹, 262144, F₆₄, 21) (dual of [262144, 262083, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(64², 11, F₆₄, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
        discarding factors / shortening the dual code based on linear OA(64², 64, F₆₄, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
        Reedâ€“Solomon code RS(62,64) [i]

(144−24, 144, 607428)-Net over F₈ — Digital

Digital (120, 144, 607428)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−24, 144, large)-Net in Base 8 — Upper bound on s

There is no (120, 144, large)-net in base 8, because

22 times m-reduction [i] would yield (120, 122, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]