MinT - Best Known (66, 66+36, s)-Nets in Base 8

Best Known (66, 66+36, s)-Nets in Base 8

(66, 66+36, 354)-Net over F₈ — Constructive and digital

Digital (66, 102, 354)-net over F₈, using

16 times m-reduction [i] based on digital (66, 118, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 59, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(66, 66+36, 518)-Net in Base 8 — Constructive

(66, 102, 518)-net in base 8, using

trace code for nets [i] based on (15, 51, 259)-net in base 64, using
- 1 times m-reduction [i] based on (15, 52, 259)-net in base 64, using
  - base change [i] based on digital (2, 39, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(66, 66+36, 869)-Net over F₈ — Digital

Digital (66, 102, 869)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+36, 141419)-Net in Base 8 — Upper bound on s

There is no (66, 102, 141420)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 130 385906 532672 934453 199205 487841 870182 971442 952153 388839 361433 026869 903062 434246 382070 623930 > 8¹⁰² [i]