MinT - Best Known (110−85, 110, s)-Nets in Base 32

Best Known (110−85, 110, s)-Nets in Base 32

(110−85, 110, 120)-Net over F₃₂ — Constructive and digital

Digital (25, 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]

(110−85, 110, 128)-Net in Base 32 — Constructive

(25, 110, 128)-net in base 32, using

32² times duplication [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]

(110−85, 110, 225)-Net over F₃₂ — Digital

Digital (25, 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]

(110−85, 110, 4270)-Net in Base 32 — Upper bound on s

There is no (25, 110, 4271)-net in base 32, because

1 times m-reduction [i] would yield (25, 109, 4271)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 116 078681 992311 632314 781485 736083 611687 990445 011672 135010 940157 201988 181343 955610 623677 923543 909859 783341 628377 701632 824695 755065 475524 554184 963506 441753 033563 029773 > 32¹⁰⁹ [i]