MinT - Best Known (110−84, 110, s)-Nets in Base 32

Best Known (110−84, 110, s)-Nets in Base 32

(110−84, 110, 120)-Net over F₃₂ — Constructive and digital

Digital (26, 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]

(110−84, 110, 128)-Net in Base 32 — Constructive

(26, 110, 128)-net in base 32, using

32² times duplication [i] based on (24, 108, 128)-net in base 32, using
- t-expansion [i] based on (23, 108, 128)-net in base 32, using
  - base change [i] based on digital (5, 90, 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]

(110−84, 110, 225)-Net over F₃₂ — Digital

Digital (26, 110, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 110, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(110−84, 110, 4639)-Net in Base 32 — Upper bound on s

There is no (26, 110, 4640)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3705 907935 713544 281733 202727 663143 671712 245487 653394 808509 997496 161852 010546 712464 381126 436118 898956 025921 902305 882206 465562 129546 256438 002246 362455 163664 905581 415376 > 32¹¹⁰ [i]