MinT - Best Known (64, 64+46, s)-Nets in Base 32

Best Known (64, 64+46, s)-Nets in Base 32

(64, 64+46, 316)-Net over F₃₂ — Constructive and digital

Digital (64, 110, 316)-net over F₃₂, using

t-expansion [i] based on digital (63, 110, 316)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 22, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
        a function field by SÃ©mirat [i]
  2. digital (7, 30, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (11, 58, 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]

(64, 64+46, 513)-Net in Base 32 — Constructive

(64, 110, 513)-net in base 32, using

32² times duplication [i] based on (62, 108, 513)-net in base 32, using
- t-expansion [i] based on (46, 108, 513)-net in base 32, using
  - base change [i] based on digital (28, 90, 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]

(64, 64+46, 2739)-Net over F₃₂ — Digital

Digital (64, 110, 2739)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+46, 4804375)-Net in Base 32 — Upper bound on s

There is no (64, 110, 4804376)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3685 527744 896070 780103 305040 144794 507914 310094 198610 389200 848614 908299 302653 267696 143864 814064 665377 486543 404445 037165 564558 290130 992150 437757 716353 944547 182975 404143 > 32¹¹⁰ [i]