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

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

(32, 32+78, 120)-Net over F₃₂ — Constructive and digital

Digital (32, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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]

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

(32, 110, 177)-net in base 32, using

32² times duplication [i] based on (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]

(32, 32+78, 273)-Net over F₃₂ — Digital

Digital (32, 110, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 110, 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]

(32, 32+78, 8716)-Net in Base 32 — Upper bound on s

There is no (32, 110, 8717)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3690 904702 041550 953337 893449 785121 227424 598680 534171 731984 961719 582054 140566 334784 507468 019177 761944 759625 384573 315280 937095 624851 562505 021680 653916 893909 981109 447040 > 32¹¹⁰ [i]