MinT - Best Known (109−77, 109, s)-Nets in Base 32

Best Known (109−77, 109, s)-Nets in Base 32

(109−77, 109, 120)-Net over F₃₂ — Constructive and digital

Digital (32, 109, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 109, 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]

(109−77, 109, 177)-Net in Base 32 — Constructive

(32, 109, 177)-net in base 32, using

32¹ times duplication [i] based on (31, 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]

(109−77, 109, 273)-Net over F₃₂ — Digital

Digital (32, 109, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 109, 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]

(109−77, 109, 9168)-Net in Base 32 — Upper bound on s

There is no (32, 109, 9169)-net in base 32, because

1 times m-reduction [i] would yield (32, 108, 9169)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 605028 324595 461107 028916 064451 663789 754910 992313 161653 111403 160496 379319 576130 591679 769154 516903 228518 840226 948677 083854 197032 866858 698370 630336 640342 232259 293136 > 32¹⁰⁸ [i]