MinT - Best Known (102, 102+40, s)-Nets in Base 8

Best Known (102, 102+40, s)-Nets in Base 8

Digital (102, 142, 1026)-net over F₈, using

6 times m-reduction [i] based on digital (102, 148, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 74, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

Digital (102, 142, 4305)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8¹⁴², 4305, F₈, 40) (dual of [4305, 4163, 41]-code), using
- 208 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 53 times 0, 1, 153 times 0) [i] based on linear OA(8¹⁴⁰, 4095, F₈, 40) (dual of [4095, 3955, 41]-code), using
  - 1 times truncation [i] based on linear OA(8¹⁴¹, 4096, F₈, 41) (dual of [4096, 3955, 42]-code), using
    - an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 8⁴âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]

There is no (102, 142, 3062989)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 292580 163922 324032 278746 096201 961119 956465 544165 141084 584077 309368 395656 388313 152028 057500 752737 069926 353871 743645 273100 917684 > 8¹⁴² [i]