MinT - Best Known (108−78, 108, s)-Nets in Base 32

Best Known (108−78, 108, s)-Nets in Base 32

(108−78, 108, 120)-Net over F₃₂ — Constructive and digital

Digital (30, 108, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 108, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(108−78, 108, 177)-Net in Base 32 — Constructive

(30, 108, 177)-net in base 32, using

t-expansion [i] based on (25, 108, 177)-net in base 32, using
- base change [i] based on digital (7, 90, 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]

(108−78, 108, 273)-Net over F₃₂ — Digital

Digital (30, 108, 273)-net over F₃₂, using

net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
  - a curve from the manYPoints database [i]

(108−78, 108, 7294)-Net in Base 32 — Upper bound on s

There is no (30, 108, 7295)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 617841 639762 987579 114600 996836 691834 311327 347454 626476 557918 303494 475499 086787 795426 349768 687784 074357 840734 014240 029145 862444 036910 630161 954215 621920 134207 205992 > 32¹⁰⁸ [i]