MinT - Best Known (173−80, 173, s)-Nets in Base 8

Best Known (173−80, 173, s)-Nets in Base 8

(173−80, 173, 256)-Net over F₈ — Constructive and digital

Digital (93, 173, 256)-net over F₈, using

8¹ times duplication [i] based on digital (92, 172, 256)-net over F₈, using
- t-expansion [i] based on digital (91, 172, 256)-net over F₈, using
  - trace code for nets [i] based on digital (5, 86, 128)-net over F₆₄, using
    - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
        a function field by SÃ©mirat [i]

(173−80, 173, 382)-Net over F₈ — Digital

Digital (93, 173, 382)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−80, 173, 18111)-Net in Base 8 — Upper bound on s

There is no (93, 173, 18112)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 718263 080165 238106 973837 556149 800528 089000 187575 113622 666641 989903 776370 159216 123812 803902 504718 759004 551563 955568 214315 207699 818777 821265 459090 762291 845231 > 8¹⁷³ [i]