MinT - Best Known (60−14, 60, s)-Nets in Base 8

Best Known (60−14, 60, s)-Nets in Base 8

(60−14, 60, 1173)-Net over F₈ — Constructive and digital

Digital (46, 60, 1173)-net over F₈, using

net defined by OOA [i] based on linear OOA(8⁶⁰, 1173, F₈, 14, 14) (dual of [(1173, 14), 16362, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(8⁶⁰, 8211, F₈, 14) (dual of [8211, 8151, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁶⁰, 8214, F₈, 14) (dual of [8214, 8154, 15]-code), using
    - trace code [i] based on linear OA(64³⁰, 4107, F₆₄, 14) (dual of [4107, 4077, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(9) [i] based on
        linear OA(64²⁷, 4096, F₆₄, 14) (dual of [4096, 4069, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(64¹⁹, 4096, F₆₄, 10) (dual of [4096, 4077, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(64³, 11, F₆₄, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
        discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
        Reedâ€“Solomon code RS(61,64) [i]

(60−14, 60, 11930)-Net over F₈ — Digital

Digital (46, 60, 11930)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(60−14, 60, large)-Net in Base 8 — Upper bound on s

There is no (46, 60, large)-net in base 8, because

12 times m-reduction [i] would yield (46, 48, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]