MinT - Best Known (96−16, 96, s)-Nets in Base 8

Best Known (96−16, 96, s)-Nets in Base 8

(96−16, 96, 65538)-Net over F₈ — Constructive and digital

Digital (80, 96, 65538)-net over F₈, using

net defined by OOA [i] based on linear OOA(8⁹⁶, 65538, F₈, 16, 16) (dual of [(65538, 16), 1048512, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(8⁹⁶, 524304, F₈, 16) (dual of [524304, 524208, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁹⁶, 524310, F₈, 16) (dual of [524310, 524214, 17]-code), using
    - trace code [i] based on linear OA(64⁴⁸, 262155, F₆₄, 16) (dual of [262155, 262107, 17]-code), using
      - constructionÂ X applied to C_e(15) âŠ‚ C_e(12) [i] based on
        linear OA(64⁴⁶, 262144, F₆₄, 16) (dual of [262144, 262098, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(64³⁷, 262144, F₆₄, 13) (dual of [262144, 262107, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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]

(96−16, 96, 552650)-Net over F₈ — Digital

Digital (80, 96, 552650)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−16, 96, large)-Net in Base 8 — Upper bound on s

There is no (80, 96, large)-net in base 8, because

14 times m-reduction [i] would yield (80, 82, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]